09年SOA北美精算师考试第二门FM官方样题第一部分(主要是金融数学)答案

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金融精算考试题及答案解析

金融精算考试题及答案解析

金融精算考试题及答案解析一、单项选择题(每题2分,共20分)1. 精算学中,用于评估未来现金流的现值的折现率是()。

A. 市场利率B. 风险利率C. 无风险利率D. 预期收益率答案:C2. 在寿险精算中,死亡率表的主要作用是()。

A. 预测未来的疾病发生率B. 计算保险产品的定价C. 评估保险公司的财务状况D. 确定保险合同的条款答案:B3. 以下哪项不是寿险精算中常用的生命表类型()。

A. 选择表B. 经验表C. 综合表D. 精算表答案:D4. 年金现值的计算公式为()。

A. PV = P * (1 + r)^nB. PV = P / (1 + r)^nC. PV = P * (1 - (1 + r)^-n) / rD. PV = P / (1 - (1 + r)^-n) * r答案:C5. 以下哪项是金融衍生品的基本功能()。

A. 风险转移B. 资产增值C. 投资组合管理D. 以上都是答案:D6. 以下哪项不是金融监管的主要目的()。

A. 保护投资者B. 维护市场稳定C. 促进金融创新D. 预防和控制金融风险答案:C7. 以下哪项是债券定价的基本原理()。

A. 债券价格等于其未来现金流的现值B. 债券价格与其票息率成正比C. 债券价格与其到期收益率成反比D. 债券价格与其信用等级成正比答案:A8. 以下哪项是信用风险管理的主要工具()。

A. 信用评级B. 信用衍生品C. 信用保险D. 以上都是答案:D9. 以下哪项是金融工程的主要应用领域()。

A. 资产证券化B. 风险管理C. 金融产品设计D. 以上都是答案:D10. 以下哪项是金融市场的基本功能()。

A. 资金筹集B. 价格发现C. 风险管理D. 以上都是答案:D二、多项选择题(每题3分,共15分)1. 精算师在进行寿险产品定价时需要考虑的因素包括()。

A. 死亡率B. 投资收益率C. 管理费用D. 税收政策答案:ABCD2. 以下哪些属于金融市场的参与者()。

09年SOA北美精算师考试第二门FM官方样题第一部分(主要是金融数学)答案

09年SOA北美精算师考试第二门FM官方样题第一部分(主要是金融数学)答案

09年SOA北美精算师考试第二门FM官方样题第一部分(主要是金融数学)答案SAMPLE SOLUTIONS FOR DERIVATIVES MARKETSQuestion #1Answer is DIf the call is at-the-money, the put option with the same cost will have a higher strike price.A purchased collar requires that the put have a lower strike price. (Page 76)Question #2Answer is C66.59 – 18.64 = 500 – K exp(–0.06) for K = 480 (Page 69)Question #3Answer is DThe accumulated cost of the hedge is (84.30-74.80)exp(.06) = 10.09.Let x be the market price.If x < 0.12 the put is in the money and the payoff is 10,000(0.12 – x) = 1,200 – 10,000x. The sale of the jalapenos has a payoff of 10,000x –1,000 for a profit of 1,200 –10,000x + 10,000x – 1,000 – 10.09 = 190.From 0.12 to 0.14 neither option has a payoff and the profit is 10,000x – 1,000 – 10.09 = 10,000x – 1,010.If x >0.14 the call is in the money and the payoff is –10,000(x – 0.14) = 1,400 – 10,000x. The profit is 1,400 – 10,000x + 10,000x – 1,000 – 10.09 = 390.The range is 190 to 390. (Pages 33-41)Question #4Answer is BThe present value of the forward prices is 10,000(3.89)/1.06 + 15,000(4.11)/1.0652 +20,000(4.16)/1.073 = 158,968. Any sequence of payments with that present value is acceptable. All but B have that value. (Page 248)Question #5Answer is EIf the index exceeds 1,025, you will receive x – 1,025. After buying the index for x you will have spent 1,025. If the index is below 1,025, you will pay 1,025 – x and after buying the index for x you will have spent 1,025. One way to get the cost is to note that the forward price is 1,000(1.05) = 1,050. You want to pay 25 less and so must spend 25/1.05 = 23.81 today. (Page 112) Question #6Answer is EIn general, an investor should be compensated for time and risk. A forward contract has no investment, so the extra 5 represents the risk premium. Those who buy the stock expect to earn both the risk premium and the time value of their purchase and thus the expected stock value is greater than 100 + 5 = 105. (Page 140)Question #7Answer is CAll four of answers A-D are methods of acquiring the stock. The prepaid forward has the payment at time 0 and the delivery at time T. (Pages 128-129)Question #8Answer is BOnly straddles use at-the-money options and buying is correct for this speculation. (Page 78)Question #9Answer is DThis is based on Exercise 3.18 on Page 89. To see that D does not produce the desired outcome, begin with the case where the stock price is S and is below 90. The payoff is S + 0 + (110 – S) –2(100 – S) = 2S – 90 which is not constant and so cannot produce the given diagram. On the other hand, for example, answer E hasa payoff of S + (90 – S) + 0 – 2(0) = 90. The cost is 100 + 0.24 +2.17 – 2(6.80) = 88.81. With interest it is 93.36. The profit is 90 –93.36 = –3.36 which matches the diagram.Question #10Answer is D[rationale-a] True, since forward contracts have no initial premium[rationale-b] True, both payoffs and profits of long forwards are opposite to short forwards.[rationale-c] True, to invest in the stock, one must borrow 100 at t=0, and then pay back 110 = 100*(1+.1) at t=1, which is like buying a forward at t=1 for 110. [rationale-d] False, repeating the calculation shown above in part c), but with 10% as a continuously compounded rate, the stock investor must now pay back100*e.1 = 110.52 at t=1; this is more expensive than buying a forward at t=1for 110.00.[rationale-e] True, the calculation would be the same as shown above in part c), but now the stock investor gets an additional dividend of 3.00 at t=.5, which theforward investor does not receive (due to not owning the stock until t=1). [This is based on Exercise 2-7 on p.54-55 ofMcDonald][McDonald, Chapter 2, p.21-28]Question #11Answer is CSolution: The 35-strike call has future cost (at t=1) of 9.12*(1+.08) = 9.85The 40-strike call has future cost (at t=1) of 6.22*(1+.08) = 6.72The 45-strike call has future cost (at t=1) of 4.08*(1+.08) = 4.41If S1<35, the profits of the 3 calls, respectively, are -9.85, -6.72, and -4.41.If 35<s1<="" -6.72,="" 3="" and="" are="" bdsfid="114" calls,="" of="" p="" profits="" respectively,="" s1-44.85,="" the=""></s1If 40<s1<="" 3="" and="" are="" bdsfid="116" calls,="" of="" p="" profits="" respectively,="" s1-44.85,="" s1-46.72,="" the=""></s1If S1>45, the profits of the 3 calls, respectively, are S1-44.85, S1-46.72, and S1-49.41.The cutoff points for when the relative profit ranking of the 3 calls change are:S1-44.85=-6.72, S1-44.85=-4.41, and S1-46.72=-4.41, yielding cutoffs of 38.13, 40.44, and 42.31.If S1<38.13, the 45-strike call has the highest profit, and the 35-strike call the lowest.If 38.13<s1<="" p="" profit,="" the=""></s1If 40.44<s1<="" p="" profit,="" the=""></s1If S1<42.31, the 35-strike call has the highest profit, and the 45-strike call the lowest.We are looking for the case where the 35-strike call has the highest profit, and the 40-strike call has the lowest profit, which occurs when S1 is between 40.44 and 42.31.[This is based on Exercise 2-13 on p.55-56 of McDonald][McDonald, Chapter 2, p.33-37]Question #12Answer is BSolution: The put premium has future value (at t=.5) of 74.20 * (1+(.04/2)) = 75.68 Then, the 6-month profit on a long put position is: max(1,000-S.5,0)-75.68. Correspondingly, the 6-month profit on a short put position is 75.68-max(1,000-S.5,0). These two profits are opposites (naturally, since long and short positions have opposite payoff and profit). Thus, they can only be equal if producing 0 profit. 0 profit is only obtained if 75.68 = max(1,000-S.5,0), or 1,000-S.5 = 75.68, or S.5 = 924.32. [McDonald, Chapter 2, p.39-42]Question #13Answer is DSolution: Buying a call, in conjunction with a short position in a stock index, is a form of insurance called a cap. Answers (A) and (B) are incorrect because they relate to a floor, which is the purchase of a put to insure against a long position in a stock index. Answer (E) is incorrect because it relates to writing a covered call, which is the sale of a call along with a long position in the stock index, so that the investor is selling rather than buying insurance. Note that a cap can also be thought of as ‘buying’ a covered call. Now, let’s calculate the profit: 2-year profit = payoff at time 2 – the future value of the initial cost to establish the position = (-75 + max(75-60,0)) –(-50 + 10)*(1+.03)2 = -75+15+40*(1.03)2 = 42.44-60 = -17.56. Thus,we’ve lost more from holding the short position in the index (since the index went up) than we’ve gained from owning the long call option.[McDonald, Chapter 3, p.59-65]Question #14Answer is ASolution: This consists of standard applications of the put-call parity equation on p.69. Let C be the price for the 40-strike call option. Then, C + 3.35 is the price for the 35-strike call option. Similarly, let P be the price for the 40-strike put option. Then, P –x is the price for the 35-strike put option, where x is what we’re trying to find. Using put-call parity, we have:(C + 3.35) + 35*e-.02 - 40 = P – x (this is for the 35-strike options)C + 40*e-.02 – 40 = P (this is for the 40-strike options)Subtracting the first equation from the second, 5*e-.02 – 3.35 = x = 1.55.[McDonald, Chapter 3, p.68-69]Answer is CSolution: The initial cost to establish this position is 5*2.78 –3*6.13 = -4.49. Thus, you are receiving 4.49 up front. This grows to 4.49*e .08*.25 = 4.58 after 3 months. Then, the following payoff/profit table can be constructed at T=.25 years: S T : 5*max(S T – 40, 0) – 3*max(S T – 35, 0) + 4.58 = Profit S T <35 0 - 0 + 4.58 = 4.58 35 <= S T <= 40 0 - 3*(S T – 35) + 4.58 = 109.58-3S T S T > 40 5*(S T -40) - 3*(S T – 35) + 4.58 = 2S T -90.42Thus, the maximum profit is unlimited (as S T increases beyond 40, so does the profit) Also, the maximum loss is 10.42(occurs at S T = 40, where profit = 109.58-120 = -10.42) [Notes] The above problem is an example of a ratio spread.[McDonald, Chapter 3, p.73]Question #16Answer is DSolution: The ‘straddle’ consists of buying a 40-strike call and buying a 40-strike put. This costs 2.78 + 1.99 = 4.77 at t=0, and grows to 4.77*e .02 = 4.87 at t=.25. The ‘strangle’ consists of buying a 35-strike put and a 45-strike call. This costs 0.44 + 0.97 = 1.41 at t=0, and grows to 1.41*e .02 = 1.44 at t=.25. For S T <40, the ‘straddle’ has a profit of 40-S T -4.87 = 35.13, and for S T >=40, the ‘straddle’ has a profit of S T -40-4.87 = 44.87. For S T <35, the ‘strangle’ has a profit of 35-S T -1.44 = 33.56, and for S T >45, the ‘strangle’ has a profit of S T -45-1.44 = 46.44. However, for 35<=S T <=45, the ‘strangle’ has a profit of -1.44 (since both options would not be exercised). Comparing the payoff structures between the ‘straddle’ and ‘strangle,’ we see that if S T <35 or if S T >45, the ‘straddle’ would outperform the ‘strangle’ (since 35.13 > 33.56,and since -44.87 > -46.44). However, if 35<=S T <=45, we can solve for the two cutoff points for S T , where the ‘strangle’ would outperform the ‘straddle’ as follows:-1.44 > 35.13 – S T, and -1.44 > S T - 44.87. The first inequality gives S T > 36.57, and the second inequality gives S T < 43.43. Thus, 36.57 < S T < 43.43.[McDonald, Chapter 3, p.78-80]Answer is B[rationale I] Yes, since Strategy I is a bear spread using calls, and bear spreads perform better when the prices of the underlying asset goes down.[rationale II] Yes, since Strategy II is also a bear spread – it just uses puts instead! [rationale III] No, since Strategy III is a box spread, which has no price risk; thus, the payoff is the same (1,000-950 = 50), no matter what the price of theunderlying asset.[Note]: An alternative, but much longer, solution is to develop payoff tables for all 3 strategies.[McDonald, Chapter 3, p.70-73]Question #18Answer is BSolution: First, let’s calculate the expected one-year profit without using the forward. This would be .2*(700+150-750) + .5(700+170-850) + .3*(700+190-950) = 20 + 10 - 18 = 12. Next, let’s calculate the expected one-year profit when buying the 1-year forward for 850. This would be 1*(700+170-850) = 20. Thus, the expected profit increases by 20 - 12 = 8 as a result of using the forward.[This is based on Exercise 4-7 on p.122 of McDonald][McDonald, Chapter 4, p.98-100]Question #19Answer is DSolution: There are 3 cases, one for each row in the above probability table.For all 3 cases, the future value of the put premium (at t=1) = 100*e.06 = 106.18.In Case 1, the 1-year profit would be: 750 - 800 - 106.18 + max(900-750,0) = -6.18In Case 2, the 1-year profit would be: 850 - 800 - 106.18 + max(900-850,0) = -6.18In Case 3, the 1-year profit would be: 950 - 800 - 106.18 +max(900-950,0) = 43.82 Thus, the expected 1-year profit = .7 * -6.18 + .3 * 43.82 = -4.326 + 13.146 = 8.82.[This is based on Exercise 4-3 on p.121 of McDonald][McDonald, Chapter 4, p.92-96]Answer is BSolution: This is an example of pricing a forward contract using discrete dividends. Thus, we need the future value of the current stock price minus the future value of each of the 12 dividends, where the valuation date is T=3. Thus, the valuation equation is: Forward price = 200*e.04(3) –[1.50*e.04(2.75) + 1.50*1.01*e.04(2.5) + 1.50*(1.01)2*e.04(2.25) + …1.50*(1.01)12] = 200*e.12 - 1.50*e.11{[1-(1.01*e-.01)12]/[1-(1.01*e.01)]}, using the geometric series formula from interest theory. This simplifies numerically to 225.50 -1.67442*11.99666 = 205.41.[This problem combines the material from interest theory and derivatives, although one could also simplify the above expression by brute force (instead of geometric series), since there are only 12 dividends to accumulate forward to T=3.] [McDonald, Chapter 5, p.133-134]Question #21Answer is ESolution: Here, the fair value of the forward contract is given by S0 * e(r-d)T =110 * e(.05-.02).5 = 110 * e.015 = 111.66. This is 0.34 less than the observed price. Thus, one could exploit this arbitrage opportunity by selling the observed forward at 112 and buying a synthetic forward at 111.66, making 112-111.66 = 0.34 profit.[This is based on Exercise 5-8 on p.163-164 of McDonald][McDonald, Chapter 5, p.135-138]Answer is BSolution: First, we must determine the present value of the forward contracts. On a per ton basis, this is: 1,600/1.05 + 1,700/(1.055)2 + 1,800/(1.06)3 = 4,562.49.Then, we must solve for the level swap price, which is labeled x below, as follows:4,562.49 = x/1.05 + x/(1.055)2 + x/(1.06)3 = x*[1/1.05 + 1/(1.055)2 + 1/(1.06)3] =2.69045*x.Thus, x = 4,562.49 / 2.69045 = 1,695.81.Thus, the amount he would receive each year is 50*1,695.81 = 84,790.38. [McDonald, Chapter 8, p.247-248]Question #23Answer is ESolution: First, note that the notional amount and the future 1-year LIBOR rates (not given) do not factor into the calculation of the swap’s fixed rate. All we need at the various zero-coupon bond prices P(0, t) for t=1,2,3,4,5, along with the 1-year implied forward rates, which are given by r0(t-1,t), for t=1,2,3,4,5. These calculations are shown in the following table:t 1 2 3 4 5P(0,t) (1.04)-1(1.045)-2 (1.0525)-3 (1.0625)-4 (1.075)-5=.96154 =.91573 =.85770 =.78466 =.69656 r0(t-1,t) s1[1.0452/1.04]-1 [1.05253/1.0452]-1 [1.06254/1.05253]-1 [1.0755/1.06254]-1 =.04000 =.05002 =.06766 =.09307 =.12649 Thus, the fixed swap rate = R = [(.96154)*(.04)+…+(.69656)*(.12649)] / [.96154 +…+.69656]= [.03846 + .04580 + .05803 + .07303 + .08811]/[.96154 + .91573 + .85770 + .78466 +.69656]= .30344 / 4.21619 = .07197 = 7.20% (approximately).[Note: This is much less calculation-intensive if you realize that the numerator (.30344) for R can also be obtained by taking 1- P(0,n) = 1 – P(0,5) = 1 - .69656 = .30344. Then, you would not need to calculate any of the implied forward rates!][McDonald, Chapter 8, p.255-258]Answer is D[rationale-a] True, hedging reduces the risk of loss, which is a primary function of derivatives.[rationale-b] True, derivatives can be used the hedge some risks that could result in bankruptcy.[rationale-c] True, derivatives can provide a lower-cost way to effect a financialtransaction.[rationale-d] False, derivatives are often used to avoid these types of restrictions. [rationale-e] True, an insurance contract can be thought of as a hedge against the risk of loss.[McDonald, Chapter 1, p.2-3]Question #25Answer is C[rationale-a] True, both types of individuals are involved in the risk-sharing process. [rationale-b] True, this is the primary reason reinsurance companies exist.[rationale-c] False, reinsurance companies share risk by issuing rather than investing in catastrophic bonds. In effect, they are ceding this excess risk to thebondholder.[rationale-d] True, it is diversifiable risk which is reduced or eliminated when risks are shared.[rationale-e] True, this is a fundamental idea underlying risk management andderivatives.[McDonald, Chapter 1, p.5-6]Question #26Answer is B[rationale-I] True, the forward seller has unlimited exposure if the underlying asset’s price increases.[rationale-II] True, the call issuer has unlimited exposure if the underlying asset’s price rises.[rationale-III] False, the maximum loss on selling a put is FV(put premium) – strike price. [McDonald, Chapter 2, p.43 (Table 2.4)]Answer is A[rationale-I] True, as prices go down, the value of holding a put option increases.canbe thought of as a put option.insuranceHomeowner’s[rationale-II] False, returns from equity-linked CDs are zero if prices decline, but positive if prices rise. Thus, owners of these CDs benefit from rising prices. [rationale-III] False, a synthetic forward consists of a long call and a short put, both of which benefit from rising prices (so the net position also benefits as such). [McDonald, Chapter 2, p.44-48]Question #28Answer is E[rationale-a] True, derivatives are used to shift income, thereby potentially lowering taxes.[rationale-b] True, as with taxes, the transfer of income lowers the probability ofbankruptcy.[rationale-c] True, hedging can safeguard reserves, and reduce the need for external financing, which has both explicit (e.g. – fees) and implicit (e.g. –reputational) costs.[rationale-d] True, when operating internationally, hedging can reduce exchange rate risk. [rationale-e] False, a firm that credibly hedges will reduce the riskiness of its cash flows, and will be able to increase debt capacity, which will lead to tax savings, since interest is deductible.[McDonald, Chapter 4, p.103-106]Question #29Answer is ASolution: If S0 is the price of the stock at time-0, then the following payments are required: Outright purchase – payment at time 0 – amount of payment = S0.Fully leveraged purchase – payment at time T – amount of payment = S0*e rT.Prepaid forward contract – payment at time 0 – amount of payment = S0*e-dT.Forward contract – payment at time T – amount of payment = S0*e(r-d)T.Since r>d>0, it must be true that S0*e-dT < S0 < S0*e(r-d)T < S0*e rT.Thus, the correct ranking is given by choice (A).[McDonald, Chapter 5, p.127-134]Answer is C[rationale-a] True, marking to market is done for futures, andcan lead to pricedifferences relative to forward contracts.[rationale-b] True, futures are more liquid; in fact, if you use the same broker to buy and sell, your position is effectively cancelled.[rationale-c] False, forwards are more customized, and futures are more standardized. [rationale-d] True, because of the daily settlement, credit risk is less with futures (v.forwards).[rationale-e] True, futures markets, like stock exchanges, do have daily price limits. [McDonald, Chapter 5, p.142]。

Bdioaq2009年度春季中国精算师资格考试

Bdioaq2009年度春季中国精算师资格考试

生命是永恒不断的创造,因为在它内部蕴含着过剩的精力,它不断流溢,越出时间和空间的界限,它不停地追求,以形形色色的自我表现的形式表现出来。

--泰戈尔2009年度春季中国精算师资格考试-考试指南第I部分中国精算师资格考试准精算师部分科目01~0901数学基础Ⅰ考试时间:3小时考试形式:客观判断题考试内容和要求:考生应掌握微积分、线性代数和运筹学的基本概念和主要内容。

A. 微积分(分数比例约为60%)1. 函数、极限、连续2. 一元函数微积分3. 多元函数微积分4. 级数5. 常微分方程B. 线性代数(分数比例约为30%)1. 行列式2. 矩阵3. 线性方程组4. 向量空间5. 特征值和特征向量6. 二次型C. 运筹学(分数比例约为10%)1. 线性规划3. 动态规划参考书目:1. 《高等数学讲义》(第二篇数学分析)樊映川编著高等教育出版社(本书可网上购买)或其他包含内容A的高等数学教材2. 《线性代数》胡显佑四川人民出版社(本书可网上购买)或其他包含内容B的线性代数教材3. 《运筹学》(修订版)1990年《运筹学》教材编写组清华大学出版社(本书可网上购买)或其他包含内容C的运筹学教材02数学基础Ⅱ考试时间:3小时考试形式:客观判断题考试内容和要求:A. 概率论(分数比例约为50%)1. 概率的计算、条件概率、全概公式和贝叶斯公式2. 随机变量的数字特征,特征函数;3. 联合分布律、边际分布函数及边际概率密度的计算4. 大数定律及其应用5. 条件期望和条件方差6. 混合型随机变量的分布函数、期望和方差等B. 数理统计(分数比例约为35%)1. 统计量及其分布2. 参数估计3. 假设检验4. 方差分析5. 列联分析C. 应用统计(分数比例约为15%)2. 时间序列分析(移动平滑,指数平滑法及ARIMA模型)参考书目:1、《概率论与数理统计》茆诗松,周纪芗编著,中国统计出版社1996年7月第1版。

2、《统计预测——方法与应用》,易丹辉编著,中国统计出版社,2001年4月第一版。

中国精算师考试《金融数学》试题(网友回忆版)二

中国精算师考试《金融数学》试题(网友回忆版)二

中国精算师考试《金融数学》试题(网友回忆版)二[单选题]1.若风险用方差度量,则下列关于投资组合的风险陈述正确的是()。

a(江南博哥).等比例投资于两只股票的组合风险比这两只股票的平均风险小b.一个完全分散化的投资组合可以消除系统风险c.相互独立的单个股票的风险决定了该股票在一个完全分散化的投资组合中的风险贡献程度A.只有a正确B.只有b正确C.只有c正确D.a,c正确E.a,b,c都不正确参考答案:A参考解析:a.设两只股票的收益率为r a和r b,对应的方差为,相关系数为,则等比例投资于两只股票的组合风险为:b.一个完全分散化的投资组合只能消除非系统风险,不能消除系统风险。

c.在一个完全分散化的投资组合中,只有来自股票间相关性的系统风险,由于股票之间相互独立,故该组合不存在风险。

[单选题]2.已知在未来三年中,银行第一年的实际利率为7.5%,第二年按计息两次的名义利率12%计息,第三年按计息四次的名义利率12.5%计息,某人为了在第三年未得到500000元的款项,第一年初需要存入银行多少?()A.365001B.365389C.366011D.366718E.367282参考答案:C参考解析:设第一年初需存入银行X元,则得:X=366010.853。

[单选题]3.一个一年期欧式看涨期权,其标的资产为一只公开交易的普通股票,已知:a.股票现价为122元b.股票年收益率标准差为0.2c.ln(股票现价/执行价现价)=0.2利用Black-scholes期权定价公式计算该期权的价格()。

A.18B.20C.22D.24E.26参考答案:D参考解析:利用Black?scholes期权定价公式可得:由得:。

于是[单选题]4.已知=5,=7,则δ=()。

A.0.0238B.0.0286C.0.0333D.0.0476E.0.0571参考答案:E参考解析:由于于是[单选题]5.某投资组合包括两只股票,已知:a.股票A的期望收益率为10%,年收益率的标准差为Z;b.股票B的期望收益率为20%,年收益率的标准差为1.5Z;c.投资组合的年收益率为12%,年收益率的标准差为Z;则股票A和股票B的收益相关系数为()。

FM-Formulas北美精算师SOA考试第二门FM公式汇总

FM-Formulas北美精算师SOA考试第二门FM公式汇总

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2009年金融联考(A)真题试卷(题后含答案及解析)

2009年金融联考(A)真题试卷(题后含答案及解析)

2009年金融联考(A)真题试卷(题后含答案及解析) 题型有:1. 单项选择题 6. 计算题9. 分析与论述题单项选择题1.如果政府大力提倡先进的机器代替劳动,这将导致( )。

A.劳动的供给曲线向右移动B.劳动的供给曲线向左移动C.劳动的需求曲线向右移动D.劳动的需求曲线向左移动正确答案:D2.( )是对凯恩斯的货币预防需求理论的发展。

A.托宾模型B.鲍莫尔模型C.惠伦模型D.卢卡斯模型正确答案:C3.下列说法正确的是( )。

A.一般情况下,总效用最大时,边际效用最小B.需求曲线斜率为正的充要条件是收入效应大于替代效应C.消费者需求曲线上的点都代表了效用最大化D.L型的无差异曲线代表了消费者对两种商品的消费都达到了饱和正确答案:C4.根据菲利普斯曲线,失业率与( )。

A.收入水平之间反方向变动B.货币工资变化率之间反方向变动C.收入水平之间同方向变动D.货币工资变化率之间同方向变动正确答案:B5.康德拉季耶夫周期是( )。

A.长周期B.中周期C.短周期D.以上都不是正确答案:A6.垄断厂商采用价格歧视的原则是( )。

A.根据不同市场的人均收入决定不同的价格B.不同市场上的边际收益分别等于厂商的边际成本C.保证边际收益高于平均收益以获得超额利润D.保证边际收益高于边际成本以获得超额利润正确答案:B7.在完全竞争的产品和要素市场中经营的厂商,设厂商以要素生产商品,其中利润达到最大的条件为( )。

A.Px=MCx,且MCx上升B.MPPa/Pa=MPPb/PbC.MPPa/Pa=MPPb/Pb=1/MCxD.MPPa/Pa=MPPb/Pb=1/MCx=1/Px正确答案:D8.消费者只购买面包和黄油,如果面包价格下降,那么( )。

A.收入效应与替代效应都引起黄油消费的上升B.收入效应与替代效应都引起黄油消费的下降C.收入效应使黄油的消费上升,但替代效应作用相反D.收入效应和替代效应将相互低效,从而商品需求保持不变正确答案:A9.如果劳动的边际产值大于工资率,可能是因为( )。

金融精算考试题及答案大全

金融精算考试题及答案大全

金融精算考试题及答案大全一、单项选择题(每题2分,共40分)1. 精算学中,以下哪项是寿险精算中的生命表?A. 经验生命表B. 理论生命表C. 人口生命表D. 经济生命表答案:A2. 以下哪个不是精算师在进行风险评估时考虑的因素?A. 死亡率B. 利率C. 通货膨胀率D. 法律风险答案:D3. 在寿险中,年金的计算不包括以下哪项?A. 即期年金B. 递延年金C. 等额年金D. 非等额年金答案:D4. 精算学中,以下哪项是用于评估保险公司偿付能力的指标?A. 偿付能力比率B. 资产负债比率C. 投资回报率D. 利润率5. 以下哪个不是精算师在产品设计时需要考虑的因素?A. 保险责任B. 定价策略C. 投资策略D. 市场趋势答案:C6. 在精算学中,以下哪项是用于评估保险合同财务状况的指标?A. 净现值B. 内部收益率C. 偿付能力充足率D. 资产负债匹配答案:A7. 以下哪个不是精算师在进行资产负债管理时需要考虑的因素?A. 资产配置B. 负债期限C. 利率风险D. 市场风险答案:D8. 在精算学中,以下哪项是用于评估保险合同盈利能力的指标?A. 利润测试B. 损失率C. 费用率D. 赔付率答案:A9. 以下哪个不是精算师在进行寿险定价时需要考虑的因素?B. 利率C. 费用率D. 投资回报率答案:D10. 在精算学中,以下哪项是用于评估保险公司财务稳定性的指标?A. 资本充足率B. 偿付能力比率C. 资产负债比率D. 利润率答案:B11. 以下哪个不是精算师在进行健康保险定价时需要考虑的因素?A. 疾病发生率B. 医疗费用C. 死亡率D. 投资回报率答案:D12. 在精算学中,以下哪项是用于评估保险合同风险的指标?A. 风险调整资本B. 偿付能力充足率C. 资产负债匹配D. 利润率答案:A13. 以下哪个不是精算师在进行非寿险定价时需要考虑的因素?A. 损失频率B. 损失严重度C. 费用率D. 投资回报率答案:D14. 在精算学中,以下哪项是用于评估保险公司盈利能力的指标?A. 净现值B. 内部收益率C. 利润率D. 资产负债比率答案:C15. 以下哪个不是精算师在进行再保险定价时需要考虑的因素?A. 再保险合同条款B. 再保险市场状况C. 再保险费用D. 投资回报率答案:D16. 在精算学中,以下哪项是用于评估保险合同公平性的指标?A. 保费充足率B. 偿付能力充足率C. 资产负债匹配D. 利润率答案:A17. 以下哪个不是精算师在进行年金定价时需要考虑的因素?A. 年金类型B. 利率C. 死亡率D. 投资回报率答案:D18. 在精算学中,以下哪项是用于评估保险合同持续性的指标?A. 持续率B. 损失率C. 费用率D. 赔付率答案:A19. 以下哪个不是精算师在进行团体保险定价时需要考虑的因素?A. 团体规模B. 团体健康状况C. 死亡率D. 投资回报率答案:D20. 在精算学中,以下哪项是用于评估保险公司流动性的指标?A. 流动比率B. 偿付能力比率C. 资产负债比率D. 利润率答案:A二、多项选择题(每题3分,共30分。

soa 北美精算师 第二门 FM TIA 样题一

soa 北美精算师 第二门 FM TIA 样题一

The Infinite Actuary’sJoint Exam2/FMSample Exam1by James Washer,FSA,MAAAlast updated-August14,2009Take this sample exam under strict exam conditions.Start a timer for3hours and stop imme-diately when the timer is done.Do not stop the clock when you go to the bathroom.Do not look at your notes.Do not look at the answer key.This exam contains35questions.Do not spend too much time on any one question.Choose the best available answer for each question.1.Which of the following is not a way to create a40-45-50butterfly?A.buy40-strike call,write two45-strike calls,buy50-strike callB.buy40-strike put,write two45-strike puts,buy50-strike putC.buy40-strike put,write45-strike call,write45-strike put,buy50-strike callD.buy40-strike call,write45-strike call,write45-strike put,buy50-strike putE.all of the above will create a40-45-50butterfly2.Letδt=14+t,0≤t≤15What is thefirst year for which the effective rate of discount is less than12.5%?A.3B.4C.5D.6E.73.A bond will pay a coupon of100at the end of each of the next three years and will pay the facevalue of1000at the end of the three-year period.The bond’s modified duration when valued using an annual effective interest rate of20%is X.Calculate X.A.2.25B.2.61C.2.70D.2.77E.2.894.You are given the following table of interest rates:CalendarYear of PortfolioOriginal RatesInvestment Investment Year Rates(in%)(in%)y i y1i y2i y3i y4i y5i y+519928.258.258.408.508.508.3519938.508.708.758.909.008.6019949.009.009.109.109.208.8519959.009.109.209.309.409.1019969.259.359.509.559.609.3519979.509.509.609.709.70199810.0010.009.909.80199910.009.809.7020009.509.5020019.00A person deposits1000on January1,1997.Let the following be the accumulated value of the 1000on January1,2000.P:under the investment year methodQ:under the portfolio yield methodCalculate P+Q.A.2575B.2595C.2610D.2655E.27005.A loan is repaid with10annual payments.Thefirst payment occurs one year after the loan.Thefirst payment is100and each subsequent payment increases by10.The annual effective rate of interest is5%.The amount of principal repaid in the4th payment is X.Determine X.A.71B.76C.80D.84E.916.A1000par value10-year bond that pays9%coupons semiannually is purchased for X.Thecoupons are reinvested at a nominal rate of7%convertible semiannually.The bond investor’s nominal annual yield rate convertible semiannually over the10-year period is9.2%.Determine X.A.924B.987C.1024D.1386E.14427.Bill writes a$100-strike call option on stock XYZ with6months to expiration for a premium of$7.24.The risk-free rate is5%convertible semiannually.For what rage of prices at expiration does Bill make a profit?A.[0,92.58)B.(92.58,∞)C.[0,107.42)D.(107.42,∞)E.[0,107.60)8.10deposits of$2000are made every other year with thefirst deposit made immediately.Theresulting fund is used to buy a perpetuity with payments made once every3years following the pattern X,4X,7X,10X,...Thefirst perpetuity payment is made3years after the last deposit of$2000.The annual effective rate of interest is6%.Determine X.A.408B.458C.471D.512E.6039.John buys a perpetuity-due with annual payments that are adjusted each year for inflation.Thefirst payment is100.Inflation is3%for years1-5and2%thereafter.Calculate the price of the perpetuity if the yield rate is an effective6%per annum.A.2750B.2760C.2770D.2780E.279010.Given the following information about the treasury market:Term Coupon Price10%96.6220%X30%88.90It is known that the2-year forward rate is4.5%.Calculate X.A.87.65B.89.70C.92.90D.93.45E.95.5011.A20-year bond is priced at par and pays R%coupons semiannually.The bond’s duration is13.95years.Determine R.A.2B.3C.4D.5E.612.Which of the following is not true?A.An asset insured with afloor is equivalent to investing in a zero-coupon bond and buying a calloption on the asset.B.A short position insured with a cap is equivalent to writing a zero-coupon bond and buying aput option on the asset.C.A covered written call is equivalent to investing in a zero-coupon bond and writing a put optionon the asset.D.A covered written put is equivalent to writing a zero-coupon bond and writing a call option onthe asset.E.All of the above are true.13.A fairly smart actuary(also know as an FSA)is offered the following rates on a loan:1.X%nominal annual rate of interest compounded monthly2.X%nominal annual rate of discount compounded monthly3.X%annual effective rate of interest4.X%annual effective rate of discount5.X%constant force of interestWhich rate does the FSA take?A.1B.2C.3D.4E.514.An annuity pays1at the beginning of each year for n ing an annual effective interestrate of i,the present value of the annuity at time0is8.55948.It is also known that(1+i)n=3.172169.Find the accumulated value of the annuity immediately after the last payment.A.27.152B.28.456C.29.324D.30.765E.31.97315.Deposits are made at the beginning of every month into a fund earning a nominal annual rateof6%convertible monthly.Thefirst deposit is100and deposit increase2%every year.In other words,deposits1-12are100,deposits13-24are100×1.02=102,deposits25-36are 100×1.022=104.04,and so on.Calculate the fund balance at the end of10years.A.16,569B.16,893C.17,257D.17,770E.17,85916.On January1a fund has a balance of$100.Sometime during the year a withdrawal of$20ismade.Immediately before the withdrawal the fund balance is$110.At year-end the balance is $95.If the time weighted and dollar weighted rates for the year are equal,then in what month was the$20withdrawal made?A.JuneB.JulyC.AugustD.SeptemberE.October17.A common stock pays annual dividends at the end of each year.The earnings per share inthe year just ended were J.Earnings are assumed to grow10%per year in the future.The percentage of earnings paid out as a dividend will be0%for the next5years and50%thereafter.Calculate the theoretical price of the stock to yield the investor21%.A.5J(1.1)4B.5J(1.1)5C.5J(1.1)6D.10J(1.1)5E.10J(1.1)618.You are the CFO of Infinite Life.Infinite Life only has one liability of$5000due in8years.Infinite Life uses a nominal rate of6%convertible semiannual to discount all liability cashflows.You call up your favorite bond broker and ask him what bonds he has for sale today.Your broker says he has5-year and10-year bonds.Both bonds are priced to yield6%convertible semiannually.The5-year bond pays6%coupons semiannually and the10-year bond is a zero-coupon bond.The bonds can be bought in any face amount.What face amount of the5-year bond should you buy in order to meet thefirst two conditions of immunization?A.777B.888C.999D.1111E.222219.You are given the following prices for$100zero-coupon bonds:Term Price195.24289.00381.63R is the swap rate in a3-year swap contract.Determine R.A.5.7%B.6.1%C.6.5%D.6.9%E.7.2%20.A fund earns simple interest of i.Which of the following are true?1.The effective rate of interest is constant for each period.2.The amount of interest is constant for each period.3.The equivalent force of interest is ln(1+i).A.1onlyB.2onlyC.3onlyD.2and3onlyE.The correct answer is not given by A,B,C or D.21.Ifδt=t1+t2,t≥0and¯I¯an=13.03567.Determine n.A.10B.11C.12D.13E.1422.You are given the following information about3funds:Fund Effective RateInterest Payments per YearA j%paid directly to investorB5%paid directly to investorC4%automatically reinvestedAn investor deposits$10,000into fund A.He reinvests fund A’s interest payments into fund B. He reinvests fund B’s interest payments into fund C.The total value of all three funds after10 years is$20,000.Determine j.A.6B.7C.8D.9E.1023.Which of the following are true?1.Modified duration is greater for bonds with higher par values.2.Modified duration is greater for yields compound more frequently.3.The modified duration of a single cashflow is the time remaining until the cashflow.A.1onlyB.2onlyC.3onlyD.2and3onlyE.The correct answer is not given by A,B,C or D.24.An annuity-immediate has the following payments:10,20,30,40,50,40,30,20,10Which of the following expressions represents the present value of the annuity?A.10a5a5B.10a5¨a5C.10a5a4D.10a5¨a4E.10(Ia)5+10(Da)425.You are given the following term structure of interest rates.TermSpot Rate(in years)1 5.00%2 5.75%3 6.25%4 6.50%rounded to the nearest100.Calculate1000(Da)4A.8700B.8800C.8900D.9000E.910026.Suppose you desire to short-sale200shares of ABC stock,which has a bid price of$24.82andan ask price of$25.01.You cover the short position three months later when the bid price is $21.45and the ask price is$21.64.Your broker charges a0.3%commission to engage in the short-sale and a0.3%commission to close the position.He also requires a50%haircut on the net proceeds of the short-sale.The market rate of interest is6%convertible continuously and the short-rebate on the haircut is4% convertible continuously.No dividends were paid on the stock during the three months.Calculate the profit on the short-sale.A.$595.60B.$608.13C.$652.33D.$671.50E.$684.1227.Which of the following are true?1.The payoffon a short forward is the spot price at expiration minus forward price.2.Zero coupon bonds can be used to shift profit diagrams.3.For forward contacts,cash settlements often reduce transaction costs.A.1onlyB.2onlyC.3onlyD.2and3onlyE.The correct answer is not given by A,B,C or D.28.A$10,000loan is repaid with level annual payments.Thefirst payment is made one year aftertaking out the loan.The outstanding balance just after the8th payment is$7,112.10.The outstanding balance just after the16th payment is$2,845.36.Calculate the outstanding balance just after the17th payment.A.$1,185B.$1,485C.$1,885D.$1,985E.$2,18529.A10-year1000par value bond pays4%coupons semiannually and is redeemable at1200.Thebond is priced to yield an annual nominal rate of6%convertible semiannually.Calculate the adjustment to the book value during the6th year.A.12.26write-upB.24.17write-downC.24.17write-upD.35.73write-downE.35.73write-up30.The present value of a25-year annuity-immediate with afirst payment of$2500and decreasingby X each year thereafter is$15,923.The annual effective rate of interest is10%.Determine X.A.70B.80C.90D.100E.11031.Which of the following expression does not represent a definition for m|a n?A.v m a nB.a m+n−a mC.v m+n s nD.v m+v m+1+...+v m+nE.All of the above represent a definition for m|a n32.At an annual effective interest rate i:(i)1grows to5in x years(ii)2grows to8in y years(iii)3grows to20in z yearsCalculate12(1+i)3x−2y+z.A.625B.650C.675D.700E.72533.Jane takes out a$100,000loan at a nominal annual rate of12%convertible monthly.Janemakes monthly interest only payments for thefirst3years and then she pays$1500per month until the loan is paid off.How many total payments does Jane make including thefinal smaller payment?A.110B.111C.142D.146E.14734.A corporation borrows10,000for25years,at an annual effective interest rate of5%.A sinkingfund is used to accumulate the principal by means of25annual deposits earning an effective annual interest rate of4%.Calculate the sum of the net amount of interest paid in the12th installment and the increment in the sinking fund for the8th year.A.676B.686C.696D.706E.71635.You are given the following prices for6-month options on S&R:Type Strike PremiumCall100093.809Put100074.201The risk-free rate is4%convertible semiannually.Calculate the six-month forward price for S&R.A.980B.1000C.1020D.1040E.1060。

中国精算师准精算师(国际金融学)历年真题试卷汇编2(题后含答案及解析)

中国精算师准精算师(国际金融学)历年真题试卷汇编2(题后含答案及解析)

中国精算师准精算师(国际金融学)历年真题试卷汇编2(题后含答案及解析)题型有:1. 单项选择题 2. 多项选择题 3. 简答题 4. 计算题 5. 论述题单项选择题1.直接标价法是一种用( )的汇率表示方法。

A.一定数量的本币表示一定单位的外币B.一定数量的外币表示一定单位的本币C.一定数量的本币表示一定单位的黄金D.一定数量的本币表示一定单位的特别提款权E.一定数量的外币表示一定单位的黄金正确答案:A解析:直接标价法是指以一定单位的外国货币作为标准,折成若干数量的本国货币来表示汇率的方法。

间接标价法是指以一定单位的本国货币为标准,折算成若干数额的外国货币来表示汇率的方法。

2.( )是按商定的汇价订立买入或卖出合约到约定日期进行交割的外汇。

A.自由外汇B.记账外汇C.远期外汇D.即期外汇E.贸易外汇正确答案:C解析:远期外汇交易,是指买卖双方成交后,并不立即办理交割,而是按照所签订的远期合同规定,在未来的约定日期办理交割的外汇交易。

按商定的汇价订立买入或卖出合约到约定日期进行交割的外汇就是远期外汇。

3.银行买入外币现钞的价格是( )。

A.买入汇率B.卖出汇率C.中间汇率D.现钞汇率E.外币汇率正确答案:D解析:现钞汇率又称现钞买卖价,是指银行买入或卖出外币现钞时所使用的汇率。

由于外国货币不能在本国流通,只能将外币兑换成本国货币才能购买本国商品,因此就有了买卖外币现钞的汇率。

4.国际收支顺差,主要是( )的结果。

A.对外贸易逆差和外资流入B.对外贸易顺差和外资流出C.对外贸易顺差和外资流入D.对外贸易逆差和外资流出E.汇率变化正确答案:C解析:国际收支顺差或称国际收支盈余是指某一国在国际收支上收入大于支出,主要是对外贸易顺差和外资流入的结果。

国际收支状况是汇率变化的直接和最主要的因素,E项因果倒置。

5.我国外汇汇率采用的是( )。

A.美元标价法B.人民币标价法C.间接标价法D.直接标价法E.双向标价法正确答案:D解析:目前世界上只有英国和美国采用间接标价法,绝大多数国家都采用直接标价法。

北美精算考试SOA第二门FM(Derivative Markets衍生品市场)知识点总结新

北美精算考试SOA第二门FM(Derivative Markets衍生品市场)知识点总结新

Premium received Asset price contingency: K>ST Maximum Loss: -K + FV(PP) Maximum Gain: FV(PP) Long with respect to underlying asset
but short with respect to derivative
price of underlying asset rises Premium received Asset price contingency: ST>K Maximum Loss: FV(PC) Maximum Gain: FV(PC)
Right, but not obligation, to sell a commodity at some future date
Profit graph is identical to that of a purchased put
Payoff graphs can be made identical by adding a zero-coupon bond to the purchased put
Long Index Payoff +
Name Long Forward
Graph
Short Forward
See above
Long Call (Purchased Call)
Short Call (Written Call)
Long Put (Purchased Put)
Description
Payoff
Profit
Comments
No premium Asset price contingency: Always Maximum Loss: Unlimited Maximum Gain: F

2009年.经济师考试《金融专业知识与实务》真题及答案解doc

2009年.经济师考试《金融专业知识与实务》真题及答案解doc

2009年(中级)经济师考试《金融专业知识与实务》真题及答案解析一、单项选择题(共60题,每题1分,每题的备选项中,只有一个最符题意的)1.在金融市场中,既是重要的资金需求者和供给者,又是金融衍生品市场上重要的套期保值主体的是()。

A.家庭B.企业C.中央银行D.政府【答案】B【解析】:企业是金融市场运行的基础,是重要的资金需求者和供给者。

此外,企业还是金融衍生品市场上重要的套期保值主体。

【试题点评】:本题考查金融市场的主体。

参见教材P92.金融工具在金融市场上能够迅速地转化为现金而不致遭受损失的能力是指金融工具的()。

A.期限性B.流动性C.收益性D.风险性【答案】B【解析】:流动性是指金融工具在金融市场上能够迅速地转化为现金而不致遭受损失的能力。

【试题点评】:本题考查金融工具流动性的概念。

参见教材P103.具有“准货币”特性的金融工具是()。

A.货币市场工具B.资本市场工具C.金融衍生品D.外汇市场工具【答案】A【解析】:货币市场中交易的金融工具一般都具有期限短、流动性高、对利率敏感等特点,具有“准货币”特性。

【试题点评】:本题考查货币市场工具的特点。

参见教材P134.在金融期权中,赋予合约买方在未来某一确定的时间或者某一时间内,以固定的价格出售相关资产的合约的形式叫()。

A.看涨期权B.欧式期权C.看跌期权D.美式期权【答案】C【解析】:看跌期权的买方有权在某一确定的时间或者某一时间内,以确定的价格出售相关资产。

【试题点评】:本题考查看跌期权的概念。

参见教材P195.在我国的债券回购市场上,回购期限是()。

A.1个月以内B.3个月以内C.6个月以内D.1年以内【答案】D【解析】:回购券种为国债和经中国人民银行批准的金融债券,回购期限在1年以下。

【试题点评】:参见教材P226.若某笔贷款的名义利率是7%,同期的市场通货膨胀率是3%,则该笔贷款的实际利率是()。

A.3%B.4%C.5%D.10%【答案】B【解析】:实际利率=名义利率-通货膨胀率=7%-3%=4%【试题点评】:本题考查实际利率、名义利率与通货膨胀率之间的关系公式。

精算师试题真题及答案解析

精算师试题真题及答案解析

精算师试题真题及答案解析精算师作为一个专业领域,要求掌握广泛的知识和技能,因此考试题目的真实性和难度一直备受关注。

本文将为大家介绍一些精算师试题的真题,并对其答案进行解析,以帮助读者更好地理解和应对这些难题。

一、寿险精算试题Question 1:某寿险公司有10000位被保险人,根据对历史数据的分析,该公司估计每年有1%的被保险人会死亡。

假设每位被保险人被认为是互相独立的风险,求该公司第二年仍然存活的人数的期望。

Answer 1:根据题目所给的信息,被保险人死亡的概率为1%,则存活的概率为99%。

由于每位被保险人被认为是互相独立的风险,所以可以将每位被保险人存活的概率进行累乘。

因此,第二年仍然存活的人数的期望为10000 * 0.99 = 9900人。

Question 2:某寿险公司根据统计数据得知,被保险人的寿命服从参数为λ的指数分布,求该公司被保险人寿命超过平均寿命的概率。

Answer 2:指数分布的概率密度函数为f(x) = λ * e^(-λx),其中λ为参数。

根据题目所给的信息,被保险人的寿命服从参数为λ的指数分布。

我们知道指数分布的平均寿命为1/λ,所以寿命超过平均寿命的概率为求解指数分布函数在平均寿命后的积分值。

具体计算过程略。

二、非寿险精算试题Question 1:某车险公司根据统计数据得知,每名驾驶员一年内发生车辆事故的次数服从参数为μ的泊松分布,且平均发生1.2次事故。

求一个驾驶员一年内发生至少2次事故的概率。

Answer 1:泊松分布的概率质量函数为P(X=k) = (e^-μ *μ^k) / k!,其中μ为参数。

根据题目所给的信息,平均发生1.2次事故,即μ=1.2。

我们需要求解一个驾驶员一年内发生至少2次事故的概率,即P(X≥2)。

具体计算过程略。

Question 2:某属性险公司的业务遵循泊松过程,每天平均有10个投保人购买该险种的保险。

已知一次购买行为的保费是100元,并且保费之间是相互独立的。

北美精算师考试试卷

北美精算师考试试卷

北美精算师考试试卷
考试科目:精算学基础
考试时间:3小时
注意事项:
1. 请在答题卡上填写您的姓名和考试编号。

2. 所有答案必须写在答题卡上,写在试卷上的任何答案无效。

3. 考试结束后,试卷和答题卡需一并上交。

第一部分:选择题(共40分)
1-10题:精算数学基础
- 1. 以下哪个不是精算学中常用的数学工具?
A. 微积分
B. 概率论
C. 线性代数
D. 统计分析
- 2. 以下哪个公式用于计算年金的现值?
A. PV = P * (1 + r)^n
B. PV = P * (1 - r)^n
C. PV = P / (1 + r)^n
D. PV = P * (1 - r^n) / r
...(此处省略其他选择题)
第二部分:简答题(共30分)
11题:请简述精算师在保险产品设计中的作用。

12题:解释什么是风险管理和精算师如何在此领域发挥作用。

...(此处省略其他简答题)
第三部分:计算题(共30分)
13题:给定一个年利率为5%的普通年金,每年支付1000美元,支付期为10年,请计算该年金的现值。

14题:一个保险公司面临两种风险:损失风险和投资风险。

请根据给定的数据,计算该公司的总风险价值。

...(此处省略其他计算题)
结束语:
考生请注意,考试结束后请立即停笔,将答题卡放在桌面上,等待监考老师收卷。

预祝您考试顺利!
请注意,以上内容仅为模拟试卷示例,实际考试内容、题型和难度可能会有所不同。

考生应根据SOA或CAS提供的官方学习材料和指南进行准备。

北美精算师 fm 教材financial mathematics习题答案 第九章

北美精算师 fm 教材financial mathematics习题答案 第九章

Solution 9.7
Since the interest rates are independent and identically distributed, we have:
E[sn ] = E [(1 + i2 )(1 + i3 )
(1 + in )] + E [(1 + i3 )(1 + i4 ) (1 + i ) + 1
E[ AVn ] = ( E [ 1 + i ]) = ( 1 + E[i ]) = 1 + i
n n
(
)
n
2
© BPP Professional Education
Solutions to practice questions – Chapter 9
Financial Mathematics
Statement IV also simplifies to the correct formula for independent and identically distributed interest rates:
If the interest rates are independent and identically distributed, then the expected accumulated value of an annuity immediate is equal to an annuity immediate calculated at the mean interest rate.
Solution 9.10
Part (i) The general formula is: E[ AVn ] = enµ + nσ For n = 2 , we have:

保险精算学概述

保险精算学概述
04
1757年,英国人简姆士·丹松首先提出应按保险人的年龄和保额收取保费,即提出保费的计算应考虑死亡率的大小。至此,精算思想正式进入人寿保险领域。
03
精算起源于人寿保险的保费计算。
1693年,英国大数学家、天文学家哈雷编制出第一张生命表,这就标志着精算学的诞生。
02
精算(起源及发展)
精算(起源及发展)
保险精算学概述
PLEASE ENTER YOUR TITLE HERE
精算 精算学(Actuarial Science ) 精算师(Actuary) 精算考试 寿险精算及非寿险 精算特点
1764年,英国的爱德沃创办了世界上第一家人寿保险公司——伦敦公平人寿保险社,采用了简姆士·丹松的计算保费的思想和方法,并设立了专门的精算技术部门,承担分析保险公司的利润来源、编制生命表、测定人口死亡率等,把精算技术作为保险经营决策的依据,使得保险公司的效益稳定、业绩领先。
01
包含三门课程:应用统计学、公司财务、经济学
02
北美精算考试-VEE课程
在线学习模块(8 modules)
02
是以网络学习为主,课本学习为辅的新一代SOA教育系统,目的在于给予精算学习者更多实务相关的教育
01
期末测试(Final Assessment)
04
期中测试(IA,Interim Assessment)
北美精算考试-初级教育考试
该课程是针对那些在学校已修过相关课程的人士,他们可以凭课程证明获得学分。对于没有在学校学习过相关课程,或者SOA不认证你所在学校所提供的课程的人士(中国大部分学校未获认证),可以通过CAS网络课程学习来获得相应的VEE学分。可关注CAS网站http:// ,通过考试的人仍可以得到VEE的学分

北美精算师科目

北美精算师科目

北美精算师科目1. 介绍北美精算师科目(Society of Actuaries Exams)是北美精算师协会(Society of Actuaries, SOA)所设立的一系列考试,用于评估个人在精算领域的专业知识和能力。

这些科目涵盖了数学、统计学、金融学和保险学等相关领域的知识,并要求考生具备良好的分析和解决问题的能力。

2. 科目设置北美精算师科目共分为两个阶段:预备科目(Preliminary Exams)和专业科目(Fellowship Exams)。

2.1 预备科目预备科目包括以下六门考试:•Exam P:概率论(Probability)•Exam FM:金融数学(Financial Mathematics)•Exam IFM:利率与金融衍生品(Investment and Financial Markets)•Exam LTAM:生命表与寿险精算(Long-Term Actuarial Mathematics)•Exam STAM:统计方法与寿险精算(Short-Term Actuarial Mathematics)•Exam SRM:风险模型与企业风险管理(Statistics for Risk Modeling)这些考试主要涵盖了概率统计、金融数学、寿险与非寿险精算等领域的知识。

考试形式为选择题和开放性问题,考试时间一般为3-4小时。

2.2 专业科目通过预备科目后,考生可以选择进入专业科目阶段,根据自己的兴趣和职业发展方向选择相应的科目。

专业科目包括以下几个领域:•Fellowship Track:这是最常见的专业科目阶段,包括Fellowship级别的考试。

•General Insurance Track:这是一个专注于非寿险精算的领域,包括General Insurance Fellowship级别的考试。

•Group and Health Track:这是一个专注于团体与健康保险精算的领域,包括Group and Health Fellowship级别的考试。

北美精算考试SOA第二门FM(Derivative Markets衍生品市场)知识点总结

北美精算考试SOA第二门FM(Derivative Markets衍生品市场)知识点总结

Commitment to sell a commodity at some future date if the purchaser exercises the option
- Max[0, ST – K]
F - ST
Max[0, ST – K] – FV(PC)
-Max[0, ST – K] + FV(PC)
Put-call parity: Call(K,T) – Put(K,T) = PV(F0,T – K)
Purchase Call Option with Strike Price K1 and Sell Call Option with Strike Price K2, where K2>K1
{max[0, ST – K] – FV(PC)} +
{-max[0, K - ST] + FV(PP)}
Mimics long forward position, but involves premiums and uses “strike price” rather than “forward price”
Name Long Forward
Graph
Short Forward
See above
Long Call (Purchased Call)
Short Call (Written Call)
Long Put (Purchased Put)
Dents
Profit graph is identical to that of a purchased call
Payoff graphs can be made identical by adding a zero-coupon bond to the purchased call

北美精算师soa 考试资格

北美精算师soa 考试资格

北美精算师协会(SOA)的考试资格没有特定的学历或专业背景要求。

具体来说,获取ASA资格的考生需要完成以下课程和考试要求:
1. 七门考试:
- Exam P–Probability(概率论)
- Exam FM–Financial Mathematics(金融数学)
- Exam IFM- Investment and Financial Markets(投资和金融市场)
- Exam LTAM-Long Term Actuarial Mathematics(长期精算数学)
- Exam STAM - Short-term Actuarial Mathematics(短期精算数学)
- Exam SRM- Statistics for Risk Modeling(风险建模统计)
- Exam PA-Predictive Analytics(预测分析)。

2. 参加APC研讨会:在通过上述考试后,考生还需要参加APC(Associate of the Society of Actuaries)研讨会才能获得准会员资格,即ASA(Associate of the Society of Actuaries)资格。

值得一提的是,对于想要成为正式精算师FSA(Fellow of the Society of Actuaries)的考生,需要在获得ASA资格的基础上,继续完成一系列的进阶课程和考试,以及积累足够的实际工作经验。

SOA的专业资格认证体系是一个逐步深入的过程,旨在确保精算师具备必要的专业知识和实践能力。

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SAMPLE SOLUTIONS FOR DERIVATIVES MARKETSQuestion #1Answer is DIf the call is at-the-money, the put option with the same cost will have a higher strike price.A purchased collar requires that the put have a lower strike price. (Page 76)Question #2Answer is C66.59 – 18.64 = 500 – K exp(–0.06) for K = 480 (Page 69)Question #3Answer is DThe accumulated cost of the hedge is (84.30-74.80)exp(.06) = 10.09.Let x be the market price.If x < 0.12 the put is in the money and the payoff is 10,000(0.12 – x) = 1,200 – 10,000x. The sale of the jalapenos has a payoff of 10,000x – 1,000 for a profit of 1,200 – 10,000x + 10,000x – 1,000 – 10.09 = 190.From 0.12 to 0.14 neither option has a payoff and the profit is 10,000x – 1,000 – 10.09 = 10,000x – 1,010.If x >0.14 the call is in the money and the payoff is –10,000(x – 0.14) = 1,400 – 10,000x. The profit is 1,400 – 10,000x + 10,000x – 1,000 – 10.09 = 390.The range is 190 to 390. (Pages 33-41)Question #4Answer is BThe present value of the forward prices is 10,000(3.89)/1.06 + 15,000(4.11)/1.0652 +20,000(4.16)/1.073 = 158,968. Any sequence of payments with that present value is acceptable. All but B have that value. (Page 248)Question #5Answer is EIf the index exceeds 1,025, you will receive x – 1,025. After buying the index for x you will have spent 1,025. If the index is below 1,025, you will pay 1,025 – x and after buying the index for x you will have spent 1,025. One way to get the cost is to note that the forward price is 1,000(1.05) = 1,050. You want to pay 25 less and so must spend 25/1.05 = 23.81 today. (Page 112)Question #6Answer is EIn general, an investor should be compensated for time and risk. A forward contract has no investment, so the extra 5 represents the risk premium. Those who buy the stock expect to earn both the risk premium and the time value of their purchase and thus the expected stock value is greater than 100 + 5 = 105. (Page 140)Question #7Answer is CAll four of answers A-D are methods of acquiring the stock. The prepaid forward has the payment at time 0 and the delivery at time T. (Pages 128-129)Question #8Answer is BOnly straddles use at-the-money options and buying is correct for this speculation. (Page 78)Question #9Answer is DThis is based on Exercise 3.18 on Page 89. To see that D does not produce the desired outcome, begin with the case where the stock price is S and is below 90. The payoff is S + 0 + (110 – S) – 2(100 – S) = 2S – 90 which is not constant and so cannot produce the given diagram. On the other hand, for example, answer E has a payoff of S + (90 – S) + 0 – 2(0) = 90. The cost is 100 + 0.24 + 2.17 – 2(6.80) = 88.81. With interest it is 93.36. The profit is 90 – 93.36 = –3.36 which matches the diagram.Question #10Answer is D[rationale-a] True, since forward contracts have no initial premium[rationale-b] True, both payoffs and profits of long forwards are opposite to short forwards.[rationale-c] True, to invest in the stock, one must borrow 100 at t=0, and then pay back 110 = 100*(1+.1) at t=1, which is like buying a forward at t=1 for 110. [rationale-d] False, repeating the calculation shown above in part c), but with 10% as a continuously compounded rate, the stock investor must now pay back100*e.1 = 110.52 at t=1; this is more expensive than buying a forward at t=1for 110.00.[rationale-e] True, the calculation would be the same as shown above in part c), but now the stock investor gets an additional dividend of 3.00 at t=.5, which theforward investor does not receive (due to not owning the stock until t=1). [This is based on Exercise 2-7 on p.54-55 of McDonald][McDonald, Chapter 2, p.21-28]Question #11Answer is CSolution: The 35-strike call has future cost (at t=1) of 9.12*(1+.08) = 9.85The 40-strike call has future cost (at t=1) of 6.22*(1+.08) = 6.72The 45-strike call has future cost (at t=1) of 4.08*(1+.08) = 4.41If S1<35, the profits of the 3 calls, respectively, are -9.85, -6.72, and -4.41.If 35<S1<40, the profits of the 3 calls, respectively, are S1-44.85, -6.72, and -4.41.If 40<S1<45, the profits of the 3 calls, respectively, are S1-44.85, S1-46.72, and -4.41.If S1>45, the profits of the 3 calls, respectively, are S1-44.85, S1-46.72, and S1-49.41.The cutoff points for when the relative profit ranking of the 3 calls change are:S1-44.85=-6.72, S1-44.85=-4.41, and S1-46.72=-4.41, yielding cutoffs of 38.13, 40.44, and 42.31.If S1<38.13, the 45-strike call has the highest profit, and the 35-strike call the lowest.If 38.13<S1<40.44, the 45-strike call has the highest profit, and the 40-strike call the lowest.If 40.44<S1<42.31, the 35-strike call has the highest profit, and the 40-strike call the lowest.If S1<42.31, the 35-strike call has the highest profit, and the 45-strike call the lowest.We are looking for the case where the 35-strike call has the highest profit, and the 40-strike call has the lowest profit, which occurs when S1 is between 40.44 and 42.31.[This is based on Exercise 2-13 on p.55-56 of McDonald][McDonald, Chapter 2, p.33-37]Question #12Answer is BSolution: The put premium has future value (at t=.5) of 74.20 * (1+(.04/2)) = 75.68 Then, the 6-month profit on a long put position is: max(1,000-S.5,0)-75.68. Correspondingly, the 6-month profit on a short put position is 75.68-max(1,000-S.5,0). These two profits are opposites (naturally, since long and short positions have opposite payoff and profit). Thus, they can only be equal if producing 0 profit. 0 profit is only obtained if 75.68 = max(1,000-S.5,0), or 1,000-S.5 = 75.68, or S.5 = 924.32. [McDonald, Chapter 2, p.39-42]Question #13Answer is DSolution: Buying a call, in conjunction with a short position in a stock index, is a form of insurance called a cap. Answers (A) and (B) are incorrect because they relate to a floor, which is the purchase of a put to insure against a long position in a stock index. Answer (E) is incorrect because it relates to writing a covered call, which is the sale of a call along with a long position in the stock index, so that the investor is selling rather than buying insurance. Note that a cap can also be thought of as ‘buying’ a covered call. Now, let’s calculate the profit:2-year profit = payoff at time 2 – the future value of the initial cost to establish the position = (-75 + max(75-60,0)) – (-50 + 10)*(1+.03)2 = -75+15+40*(1.03)2 = 42.44-60 = -17.56. Thus, we’ve lost more from holding the short position in the index (since the index went up) than we’ve gained from owning the long call option.[McDonald, Chapter 3, p.59-65]Question #14Answer is ASolution: This consists of standard applications of the put-call parity equation on p.69. Let C be the price for the 40-strike call option. Then, C + 3.35 is the price for the 35-strike call option. Similarly, let P be the price for the 40-strike put option. Then, P – x is the price for the 35-strike put option, where x is what we’re trying to find. Using put-call parity, we have:(C + 3.35) + 35*e-.02 - 40 = P – x (this is for the 35-strike options)C + 40*e-.02 – 40 = P (this is for the 40-strike options)Subtracting the first equation from the second, 5*e-.02 – 3.35 = x = 1.55.[McDonald, Chapter 3, p.68-69]Answer is CSolution: The initial cost to establish this position is 5*2.78 – 3*6.13 = -4.49. Thus, you are receiving 4.49 up front. This grows to 4.49*e .08*.25 = 4.58 after 3 months. Then, the following payoff/profit table can be constructed at T=.25 years:S T : 5*max(S T – 40, 0) – 3*max(S T – 35, 0) + 4.58 = ProfitS T <35 0 - 0 + 4.58 = 4.58 35 <= S T <= 40 0 - 3*(S T – 35) + 4.58 = 109.58-3S T S T > 40 5*(S T -40) - 3*(S T – 35) + 4.58 = 2S T -90.42Thus, the maximum profit is unlimited (as S T increases beyond 40, so does the profit) Also, the maximum loss is 10.42 (occurs at S T = 40, where profit = 109.58-120 = -10.42)[Notes] The above problem is an example of a ratio spread.[McDonald, Chapter 3, p.73]Question #16Answer is DSolution: The ‘straddle’ consists of buying a 40-strike call and buying a 40-strike put. This costs 2.78 + 1.99 = 4.77 at t=0, and grows to 4.77*e .02 = 4.87 at t=.25. The ‘strangle’ consists of buying a 35-strike put and a 45-strike call. This costs 0.44 + 0.97 = 1.41 at t=0, and grows to 1.41*e .02 = 1.44 at t=.25. For S T <40, the ‘straddle’ has a profit of 40-S T -4.87 = 35.13, and for S T >=40, the ‘straddle’ has a profit of S T -40-4.87 = 44.87. For S T <35, the ‘strangle’ has a profit of 35-S T -1.44 = 33.56, and for S T >45, the ‘strangle’ has a profit of S T -45-1.44 = 46.44. However, for 35<=S T <=45, the ‘strangle’ has a profit of -1.44 (since both options would not be exercised). Comparing the payoff structures between the ‘straddle’ and ‘strangle,’ we see that if S T <35 or if S T >45, the ‘straddle’ would outperform the ‘strangle’ (since 35.13 > 33.56, and since -44.87 > -46.44). However, if 35<=S T <=45, we can solve for the two cutoff points for S T , where the ‘strangle’ would outperform the ‘straddle’ as follows:-1.44 > 35.13 – S T, and -1.44 > S T - 44.87. The first inequality gives S T > 36.57, and the second inequality gives S T < 43.43. Thus, 36.57 < S T < 43.43.[McDonald, Chapter 3, p.78-80]Answer is B[rationale I] Yes, since Strategy I is a bear spread using calls, and bear spreads perform better when the prices of the underlying asset goes down.[rationale II] Yes, since Strategy II is also a bear spread – it just uses puts instead! [rationale III] No, since Strategy III is a box spread, which has no price risk; thus, the payoff is the same (1,000-950 = 50), no matter what the price of theunderlying asset.[Note]: An alternative, but much longer, solution is to develop payoff tables for all 3 strategies.[McDonald, Chapter 3, p.70-73]Question #18Answer is BSolution: First, let’s calculate the expected one-year profit without using the forward. This would be .2*(700+150-750) + .5(700+170-850) + .3*(700+190-950) = 20 + 10 - 18 = 12. Next, let’s calculate the expected one-year profit when buying the 1-year forward for 850. This would be 1*(700+170-850) = 20. Thus, the expected profit increases by 20 - 12 = 8 as a result of using the forward.[This is based on Exercise 4-7 on p.122 of McDonald][McDonald, Chapter 4, p.98-100]Question #19Answer is DSolution: There are 3 cases, one for each row in the above probability table.For all 3 cases, the future value of the put premium (at t=1) = 100*e.06 = 106.18.In Case 1, the 1-year profit would be: 750 - 800 - 106.18 + max(900-750,0) = -6.18In Case 2, the 1-year profit would be: 850 - 800 - 106.18 + max(900-850,0) = -6.18In Case 3, the 1-year profit would be: 950 - 800 - 106.18 + max(900-950,0) = 43.82 Thus, the expected 1-year profit = .7 * -6.18 + .3 * 43.82 = -4.326 + 13.146 = 8.82.[This is based on Exercise 4-3 on p.121 of McDonald][McDonald, Chapter 4, p.92-96]Answer is BSolution: This is an example of pricing a forward contract using discrete dividends. Thus, we need the future value of the current stock price minus the future value of each of the 12 dividends, where the valuation date is T=3. Thus, the valuation equation is: Forward price = 200*e.04(3) – [1.50*e.04(2.75) + 1.50*1.01*e.04(2.5) + 1.50*(1.01)2*e.04(2.25) + …1.50*(1.01)12] = 200*e.12 - 1.50*e.11{[1-(1.01*e-.01)12]/[1-(1.01*e.01)]}, using the geometric series formula from interest theory. This simplifies numerically to 225.50 -1.67442*11.99666 = 205.41.[This problem combines the material from interest theory and derivatives, although one could also simplify the above expression by brute force (instead of geometric series), since there are only 12 dividends to accumulate forward to T=3.][McDonald, Chapter 5, p.133-134]Question #21Answer is ESolution: Here, the fair value of the forward contract is given by S0 * e(r-d)T =110 * e(.05-.02).5 = 110 * e.015 = 111.66. This is 0.34 less than the observed price. Thus, one could exploit this arbitrage opportunity by selling the observed forward at 112 and buying a synthetic forward at 111.66, making 112-111.66 = 0.34 profit.[This is based on Exercise 5-8 on p.163-164 of McDonald][McDonald, Chapter 5, p.135-138]Answer is BSolution: First, we must determine the present value of the forward contracts. On a per ton basis, this is: 1,600/1.05 + 1,700/(1.055)2 + 1,800/(1.06)3 = 4,562.49.Then, we must solve for the level swap price, which is labeled x below, as follows:4,562.49 = x/1.05 + x/(1.055)2 + x/(1.06)3 = x*[1/1.05 + 1/(1.055)2 + 1/(1.06)3] =2.69045*x.Thus, x = 4,562.49 / 2.69045 = 1,695.81.Thus, the amount he would receive each year is 50*1,695.81 = 84,790.38. [McDonald, Chapter 8, p.247-248]Question #23Answer is ESolution: First, note that the notional amount and the future 1-year LIBOR rates (not given) do not factor into the calculation of the swap’s fixed rate. All we need at the various zero-coupon bond prices P(0, t) for t=1,2,3,4,5, along with the 1-year implied forward rates, which are given by r0(t-1,t), for t=1,2,3,4,5. These calculations are shown in the following table:t 1 2 3 4 5P(0,t) (1.04)-1(1.045)-2 (1.0525)-3 (1.0625)-4 (1.075)-5=.96154 =.91573 =.85770 =.78466 =.69656 r0(t-1,t) s1[1.0452/1.04]-1 [1.05253/1.0452]-1 [1.06254/1.05253]-1 [1.0755/1.06254]-1 =.04000 =.05002 =.06766 =.09307 =.12649 Thus, the fixed swap rate = R = [(.96154)*(.04)+…+(.69656)*(.12649)] / [.96154 +…+.69656]= [.03846 + .04580 + .05803 + .07303 + .08811]/[.96154 + .91573 + .85770 + .78466 +.69656]= .30344 / 4.21619 = .07197 = 7.20% (approximately).[Note: This is much less calculation-intensive if you realize that the numerator (.30344) for R can also be obtained by taking 1- P(0,n) = 1 – P(0,5) = 1 - .69656 = .30344. Then, you would not need to calculate any of the implied forward rates!][McDonald, Chapter 8, p.255-258]Answer is D[rationale-a] True, hedging reduces the risk of loss, which is a primary function of derivatives.[rationale-b] True, derivatives can be used the hedge some risks that could result in bankruptcy.[rationale-c] True, derivatives can provide a lower-cost way to effect a financialtransaction.[rationale-d] False, derivatives are often used to avoid these types of restrictions. [rationale-e] True, an insurance contract can be thought of as a hedge against the risk of loss.[McDonald, Chapter 1, p.2-3]Question #25Answer is C[rationale-a] True, both types of individuals are involved in the risk-sharing process. [rationale-b] True, this is the primary reason reinsurance companies exist.[rationale-c] False, reinsurance companies share risk by issuing rather than investing in catastrophic bonds. In effect, they are ceding this excess risk to thebondholder.[rationale-d] True, it is diversifiable risk which is reduced or eliminated when risks are shared.[rationale-e] True, this is a fundamental idea underlying risk management andderivatives.[McDonald, Chapter 1, p.5-6]Question #26Answer is B[rationale-I] True, the forward seller has unlimited exposure if the underlying asset’s price increases.[rationale-II] True, the call issuer has unlimited exposure if the underlying asset’s price rises.[rationale-III] False, the maximum loss on selling a put is FV(put premium) – strike price. [McDonald, Chapter 2, p.43 (Table 2.4)]Answer is A[rationale-I] True, as prices go down, the value of holding a put option increases.canbe thought of as a put option.insuranceHomeowner’s[rationale-II] False, returns from equity-linked CDs are zero if prices decline, but positive if prices rise. Thus, owners of these CDs benefit from rising prices. [rationale-III] False, a synthetic forward consists of a long call and a short put, both of which benefit from rising prices (so the net position also benefits as such). [McDonald, Chapter 2, p.44-48]Question #28Answer is E[rationale-a] True, derivatives are used to shift income, thereby potentially lowering taxes.[rationale-b] True, as with taxes, the transfer of income lowers the probability ofbankruptcy.[rationale-c] True, hedging can safeguard reserves, and reduce the need for external financing, which has both explicit (e.g. – fees) and implicit (e.g. –reputational) costs.[rationale-d] True, when operating internationally, hedging can reduce exchange rate risk. [rationale-e] False, a firm that credibly hedges will reduce the riskiness of its cash flows, and will be able to increase debt capacity, which will lead to tax savings,since interest is deductible.[McDonald, Chapter 4, p.103-106]Question #29Answer is ASolution: If S0 is the price of the stock at time-0, then the following payments are required: Outright purchase – payment at time 0 – amount of payment = S0.Fully leveraged purchase – payment at time T – amount of payment = S0*e rT.Prepaid forward contract – payment at time 0 – amount of payment = S0*e-dT.Forward contract – payment at time T – amount of payment = S0*e(r-d)T.Since r>d>0, it must be true that S0*e-dT < S0 < S0*e(r-d)T < S0*e rT.Thus, the correct ranking is given by choice (A).[McDonald, Chapter 5, p.127-134]Question #30Answer is C[rationale-a] True, marking to market is done for futures, and can lead to pricedifferences relative to forward contracts.[rationale-b] True, futures are more liquid; in fact, if you use the same broker to buy and sell, your position is effectively cancelled.[rationale-c] False, forwards are more customized, and futures are more standardized. [rationale-d] True, because of the daily settlement, credit risk is less with futures (v.forwards).[rationale-e] True, futures markets, like stock exchanges, do have daily price limits. [McDonald, Chapter 5, p.142]11。

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