北大版金融数学引论第二章答案,DOC

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金融数学引论答案第二版

金融数学引论答案第二版【篇一：北大版金融数学引论第二章答案】>第二章习题答案1．某家庭从子女出生时开始累积大学教育费用5万元。

如果它们前十年每年底存款1000元，后十年每年底存款1000+x 元，年利率7%。

计算x 。

解：s = 1000s?7%+xs?7%20p10p20px = 50000 ? 1000s?7% = 651.72s?p7%102．价值10,000元的新车。

购买者计划分期付款方式：每月底还250元，期限4年。

月结算名利率18%。

计算首次付款金额。

解：设首次付款为x ，则有10000 = x + 250a?p1.5%48解得x = 1489.3613．设有n年期期末年金，其中年金金额为n，实利率i =n解：p v = na?npi= 1nn+2 =(n + 1)nn2n4．已知：a?pn= x，a?p2n= y 。

试用x和y 表示d 。

解： a?p2n= a?pn+ a?p (1 ? d)则nny ? xd = 1 ? ( x ) n5．已知：a?p7= 5.58238, a?= 7.88687, a?= 10.82760。

计算i。

11p18p解：a?p = a?p + a?p v718711解得=i = 6.0%10?p +a∞?p6.证明： 11?v10s。

解：p v = 100a?+ 100a20?8p3% p3% = 2189.7168．某人现年40岁，现在开始每年初在退休金帐号上存入1000元，共计25年。

然后，从65岁开始每年初领取一定的退休金，共计15年。

设前25年的年利率为8%，后15年的年利率7%。

计算每年的退休金。

解：设每年退休金为x，选择65岁年初为比较日=解得x = 8101.658。

金融数学引论答案第一章--北京大学出版[1]

第一章习题答案1•解：JEt = O 代入得A(O) = 3 于是:a(t) =A(t)/A(O)= (t 2 + 2t + 3) /3 In =A(n) 一 A(n 一 1)= (n 2 + 2n + 3) - ((n - I)2 + 2(n - 1) + 3))= 2n + l 2.解:(1)1 = A(n)-A(t) = I n +I nl + ∙ ∙ ÷I t+1 =n(n+ l)∕2-t(t+ 1)/2 (2)I = A(n)-A(t)= Y J l k = 2π+, -2,+,A-r÷l3•解：由题意得a(0) = I Z a(3) =A(3)/A(O)= => a = , b = 1 ∕∙ A(5) = 100A(IO)=A(O) ∙ a(10) = A(5) ∙ a(10)/ a(5)= 100 X 3 = 300.4.解：(l)i5 =(A(5) - A(4))∕A(4)=5120^ % ilθ =(A(IO) - A ⑼)∕A(9)=5145≈ %(2)i5 =(A(5) 一 A(4))∕A(4)IOO(I + 0.1)5-l∞(l + 0.1)4IOo(I + o.ιy l5•解:A(7) = A(4)(l + i5)(l + i6)(l + i7) =1000 XXX6•解：设年单利率为i500(1 + = 615解得i = %设500元需要累积t 年500(1 + t × %) = 630解得t = 3年4个月 }7•解：设经过t 年后，年利率达到％1 + 4%×t= (1 + 2.5%)1 t Q8. 解ι(l + i)11 = (l + i)5+2*3 = XY 39. 解：设实利辜为i600[(l + i)2 一 1] = 264解彳gi = 20%：• A(3) = 2000(1 + i)3 = 3456 元10•解：设实利站为i10% i K)=(A(10)-A(9))∕A(9) =1∞(1 + 0.1)10-100(1 + 0.1)9 IOO(I + 0.1)910%---------- 1 ------- ~ (l + z)n (l + ∕)2n所以"=导》右11•解:由500×(l+ i)30 = 4∞0 => (l + i)30 = 8IOOOO I(XX)O IOOOo++ i)2°(1 +i)40 (1 +i)60=IOOO ×2 4 (8~+8~+8^2)12 解:(1 + i)a = 2(l + i)b =j (2)(l + i)c = 5 (3)3 + i)n =- (4) 2=> n ∙ In(I. + i) = In 5 -In 3⅝l∕ ⅝l∕11/ /k 牧→ In5 = c × ln(l + i) × (2) => In3 = (a + b) ■ In (1 + i) =C -(a + b)13•解：A ∙ i = 336 A ∙ d = 300 i —d = i ∙ d => A =2800 14•解：(1)10%'1 + 5x10%=%⑵ a-1(t) = 1 一=> a(t) = a(5)III δ A(t)= δ B(t)得t = 5)19・解：依题意,累积函数为a(t) = at2 + bt + 1 a = 0.25a ++ 1 =a(l) = a + b + 1 ==> a =b =于是 δ =≤222= 0.068a(0.5)20∙解：依题意，§ A (t) = J 「J B (t)= ----------------1 + L 1 + tIllJ A (t)> ¾ (t) 1一 1-0.1/=dS = ΦH√1) a(5)=%15∙解:由(l + -r )3=(l-£-)7 3 4i⑶-3二> 〃⑷=4・[1一(1 +寸)-可:⑶ Itl:⑹ z ∕(12)(1 + L_)6=(1_L_)3) 6 12〃(⑵=> 严>=6∙[(1 -------- Γ2-l]1216•解:⑴ 终值为IOO × (1 + i(4)/4 F?=元⑵ 终值为Ioo × [(1 -4d<V4))1/4 ]-2=元17. 解：利用 1/d (FTl)- 1/i (Fn) = I∕m=> m = 818. 解:aA (t) = 1 + => δ A (t)a"1A (t) = l-0.05r=>¾ (a"1B (t))1 aΛ(t) 0.05"l-0.05ra A (I) 1 + 0」/2t 2=> -------- > ---------- 1 +L 1 +t=> t > 121.解：d (4) = 8% ,设复利下月实贴现率为d,单利下实利率为do 。

金新学案北师大高中数学选修检测：第二章概率 § 含答案

第二章§6一、选择题1．把一个正态曲线a沿着横轴方向向右移动2个单位，得到新的一条曲线b.下列说法中不正确的是()A．曲线b仍然是正态曲线B．曲线a和曲线b的最高点的纵坐标相等C．以曲线b为概率密度曲线的总体的期望比以曲线a为概率密度曲线的总体的期望大2 D．以曲线b为概率密度曲线的总体的方差比以曲线a为概率密度曲线的总体的方差大2 答案： D2．已知随机变量X服从正态分布N(2，σ2)，P(X<4)＝0.84，则P(X≤0)＝()A．0.16B．0.32C．0.68 D．0.84解析：由X～N(2，σ2)，可知其正态曲线如图所示，对称轴为x＝2，则P(X≤0)＝P(X≥4)＝1－P(X<4)＝1－0.84＝0.16.故选A．答案： A3．如图是当σ取三个不同值σ1、σ2、σ3的三种正态曲线N(0，σ2)的图像，那么σ1、σ2、σ3的大小关系是()A．σ1＞1＞σ2＞σ3＞0 B．0＜σ1＜σ2＜1＜σ3C．σ1＞σ2＞1＞σ3＞0 D．0＜σ1＜σ2＝1＜σ3解析：当μ＝0，σ＝1时，正态曲线f(x)＝12πe－x22在x＝0处取最大值12π，故σ2＝1.由正态曲线的性质，当μ一定时，曲线的形状由σ确定，当σ越小，曲线越“瘦高”，反之越“矮胖”，故选D．答案： D4．已知随机变量X ～N (0,1)，则X 在区间(－3，＋∞)内取值的概率等于( ) A ．0.887 4 B ．0.002 6 C ．0.001 3D ．0.998 7解析：由X ～N (0,1)可知，μ＝0，σ＝1. 结合密度函数的图像可知 P (X ≥－3)＝12P (－3≤X ≤3)＋12＝0.998 7. 答案： D 二、填空题5．在某项测量中，测量结果X 服从正态分布N (1，σ2)(σ>0)，若X 在(0,1)内取值的概率为0.4，则X 在(0,2)内取值的概率为____________.解析：由X ～N (1，σ2)(σ>0)，知正态曲线的对称轴为x ＝1，从而由图像可知P (0<X <1)＝P (1<X <2)，所以P (0<X <2)＝2P (0<X <1)＝2×0.4＝0.8. 答案： 0.86．已知正态总体的数据落在区间(－3，－1)里的概率和落在区间(3,5)里的概率相等，那么这个正态总体的数学期望为____________.解析：区间(－3，－1)和区间(3,5)关于x ＝1对称(－1关于x ＝1的对称点是3，－3关于x ＝1的对称点是5)，所以正态分布的数学期望就是1.答案： 1 三、解答题7．一台机床生产一种尺寸为10 mm 的零件，现在从中抽测10个，它们的尺寸分别如下(单位：mm)：10.2,10.1,10,9.8,9.9,10.3，9.7,10,9.9,10.1.如果机床生产零件的尺寸Y 服从正态分布，求正态分布的概率密度函数式．解析： μ＝ 110(10.2＋10.1＋10＋9.8＋9.9＋10.3＋9.7＋10＋9.9＋10.1)＝10， σ2＝110[(10.2－10)2＋(10.1－10)2＋(10－10)2＋(9.8－10)2＋(9.9－10)2＋(10.3－10)2＋(9.7－10)2＋(10－10)2＋(9.9－10)2＋(10.1－10)2]＝0.03.即μ＝10，σ2＝0.03.所以Y 的概率密度函数为f (x )＝ 106πe － 50(x －10)23.8．设X ～N (6,1)，求P (4<x <5)．解析：由已知μ＝6，σ＝1， ∵P (5<x <7)＝P (μ－σ<x <μ＋σ)＝0.683， P (4<x <8)＝P (μ－2σ<x <μ＋2σ)＝0.954，P (4<x <5)＋P (7<x <8)＝P (4<x <8)－P (5<x <7)＝0.271，如图：由正态曲线的对称性知 P (4<x <5)＝P (7<x <8)，∴P (4<x <5)＝12[P (4<x <8)－P (5<x <7)]尖子生题库☆☆☆9．工厂制造的某机械零件尺寸X 服从正态分布N ⎝⎛⎭⎫4，19，问在一次正常的试验中，取1 000个零件时，不属于区间(3,5)这个尺寸范围内的零件大约有多少个？解析：不属于区间(3,5)的概率为P (X ≤3)＋P (X ≥5) ＝1－P (3<X <5)＝1－P (|X －4|<1)．因为X ～N ⎝⎛⎭⎫4，19，所以，μ＝4，σ＝13，所以1－P (|X －4|<1)＝1－P (|X －μ|<3σ)＝1－0.9974 ＝0.0026≈0.003. 1000×0.003＝3(个)．即不属于(3,5)这个尺寸范围内的零件大约有3个．。

金融数学课后答案

金融数学课后答案【篇一：金融数学(利息理论)复习题练习题】购买一张3年期，面值为1000元的国库券，每年末按息票率为8%支付利息，第三年末除支付80元利息外同时偿付1000元的债券面值，如果该债券发行价为900元，请问他做这项投资是否合适？ 2.已知：1） 1?i2） 1?由于(1?m)?(1?n)?1?i 由于(1?)?(1?)?1?d3. 假设银行的年贷款利率12%，某人从银行借得期限为1年，金额为100元的贷款。

银行对借款人的还款方式有两种方案：一、要求借款人在年末还本付息；二、要求借款人每季度末支付一次利息年末还本。

试分析两种还款方式有何区别？哪一种方案对借款人有利？4. 设m?1，按从小到大的顺序排列i,i(m)(m)(m)(m)m?(1?i5)(1?i6)?1 求m?? ?(1?d(5)d(6)?1)(1?6) 求m?? 5(5)(6)d(m)mm(n)nm(n)n,d,d(m),?解：由i?d?i?d? i?dd(m?1)?d(m) ? d?d(m) i(m)?d(n) ? d(m)?i(m) i(m?1)?i(m)?i(m)?ii(m)?limd(m)?? 1?i?e??1?? ， limm??m???d?d(m)???i(m)?i5. 两项基金x,y以相同的金额开始，且有：（1）基金x以利息强度5%计息；（2）基金y以每半年计息一次的名义利率j计算；（3）第8年末，基金x中的金额是基金y中的金额的1.5倍。

求j.6. 已知年实际利率为8%，乙向银行贷款10,000元,期限为5年，计算下列三种还款方式中利息所占的额度：1）贷款的本金及利息积累值在第五年末一次还清； 2）每年末支付贷款利息，第五年末归还本金； 3）贷款每年年末均衡偿还（即次用年金方式偿还）。

三种还款方式乙方支付的利息相同吗? 请你说明原因？7.某人在前两年中，每半年初在银行存款1000元，后3年中，每季初在银行存款2000元，每月计息一次的年名义利率为12% 计算5年末代储户的存款积累值。

(完整版)北大版金融数学引论第二章答案.docx

如果它们前十年每年底存款1000元，后十年每年底存款 1000+X 元，年利率 7%。

计算 X 。

解：S = 1000s ?+ Xs ?p 7% 10 p 7%20X = 50000 - 1000s 20?p7% = 651 72s ? p7%.102．价值 10,000元的新车。

购买者计划分期付款方式：每月底还 250元，期限 4年。

月结算名利率 18%。

计算首次付款金额。

解：设首次付款为 X ，则有10000 = X + 250a 48?p1.5%解得X = 1489.363．设有 n 年期期末年金，其中年金金额为n ，实利率 i = 1。

试计算该年金的现值。

n解：P V =na?npi=1 - v nn 1n= (n + 1)n n 2- n n +2(n + 1) n4．已知： a?np= X ， a ?np= Y 。

2试用 X 和Y 表示 d 。

解： a 2? np= a? npnp(1 - d) n则1+ a?Y - X ) nd = 1 - (X5．已知： a? 7p = 5.58238, a ? p= 7.88687, a ? = 10.82760。

计算 i 。

1118 p解：a 18?p = a?7p + a 11?p v 7解得i = 6.0%6.证明： 1s10p +a ∞? p 。

解：P V = 100a?8p3% + 100a 20?p3% = 2189.7168．某人现年 40岁，现在开始每年初在退休金帐号上存入 1000元，共计 25年。

数理金融学导论补充练习及参考答案

。
6．如果一家银行所提供的利息是以名义利率5%连续地计算利息，那么每年的有效利率应该是多少？
解：有效利率应为：
。
即有效利率是每年。
7．一家公司在未来的5年中需要一种特定型号的机器。这家公司当前有1台这种机器，价值6000美元，未来3年内每年折旧2000美元，在第三年年末报废。该机器开始使用后第一年运转费用在该年年初值为9000美元，之后在此基础上每年增加2000美元。在每年的年初可以按固定价格22000美元购买1台新机器。1台新机器的寿命是6年，在最初使用的两年中每年折旧3000美元，这之后每年折旧4000美元。新机器在第一年的运转成本是6000美元，在随后的每年中将增加1000美元。如果利率为10%，公司应在何时购买新机器？
其中，
因此股票的价格为：
股票价格的现值
第三步，将从步骤1和步骤2得到的这两个现值相加得到普通股的价值。
为了验证上面所列现金流的正确性，假设公司将在第三年的年初购买新机器，则公司在第一年的成本为旧机器9000美元的运转成本；在第二年的成本为旧机器11000的运转成本；在第三年的成本为新机器22000的购买成本，加上6000美元的运转成本，再减去从替换机器中得到的2000美元；在第四年的成本是7000美元的运转成本；在第五年的成本是8000美元的运转成本；在第六年的成本是-12000美元，它是已经使用了三年的机器价值的负值。其他的三个现金流序列可以通过相似的方法推得。
解：这家公司可以在第1、2、3、4年的年初购买新机器，其对应的六年现金流如下（以1000美元为单位）：
在第一年的年初购买新机器：22，7，8，9，10，-4；
在第二年的年初购买新机器：9，24，7，8，9，-8；
在第三年的年初购买新机器：9，11，26，7，8，-12；

金融数学引论答案第一章__北京大学出版[1]

第一章习题答案1. 设总量函数为A(t) = t 2 + 2t + 3 。

试计算累积函数a(t) 和第n 个时段的利息I n 。

解: 把t = 0 代入得A(0) = 3 于是:a(t) =A(t)/A(0)=（t 2 + 2t + 3）/3I n = A(n) − A(n − 1)= (n 2 + 2n + 3) − ((n − 1)2+ 2(n − 1) + 3))= 2n + 12. 对以下两种情况计算从t 时刻到n(t < n) 时刻的利息: (1)I r (0 < r <n); (2)I r = 2r (0 < r < n).解: ()n n-1t 11I A(n)A(t)I I I n(n 1)/2t(t 1)/2+=-=+++=+-+・・・ (2)1t 11I A(n)A(t) 22n n k k t I ++=+=-==-∑3. 已知累积函数的形式为: 2a(t) at b =+。

若0 时刻投入的100 元累积到3 时刻为172 元，试计算：5 时刻投入的100 元在10 时刻的终值。

解: 由题意得a(0) = 1, a(3) =A(3)/A(0)= 1.72⇒ a = 0.08, b = 1∴ A(5) = 100A(10) = A(0) ・ a(10) = A(5) ・ a(10)/a(5)= 100 × 3 = 300.4. 分别对以下两种总量函数计算i 5 和i 10 :(1) A(t) = 100 + 5t; (2)t A(t) 100(1 0.1)=+.解：(1)i 5 =(A(5) − A(4))/A(4)=5120≈ 4.17%i 10 =(A(10) − A(9))/A(9)=5145≈ 3.45%(2)i 5 =(A(5) − A(4))/A(4)()()()544109109100(1 0.1)100(1 0.1) 10%100(1 0.1)100(1 0.1)100(1 0.1)i (A 10A 9)/A 9 10%100(1 0.1)+-+==++-+=-==+5.设()n A 4 1000, i 0.01n ==. 试计算A(7) 。

金融数学引论答案.docx

⾦融数学引论答案.docx第⼀章习题答案1.设总量函数为A(t) = t2 + 2/ + 3 o试计算累积函数a(t)和第n个吋段的利息【仇°解：把t =()代⼊得4(()) = 3于是：4(t) t? + 2t + 3啲=丽=3In = 4(北)⼀A(n⼀1)=(n2 + 2n + 3) — ((n — I)2 + 2(n — 1) + 3))= 2n+l2.对以下两种情况计算从t时刻到冗(￡ < n)时刻的利息：(1)⼛(0 < r < n);(2)/r =2r(0解：(1)I = A(n) - A(t)—In + in-1+ ? ? ? + A+l n(n + 1) t(t + 1)=2 2I = A(n) - A(t)n n=乞h = ⼟hk=t+l A：=t+13.已知累积函数的形式为：Q(t) = at2 +⼏若0时刻投⼊的100元累积到3吋刻为172元,试计算：5时刻投⼊的10()元在10时刻的终值。

解：由题意得。

(0) = 1, ?(3) = = L72=> a = 0.0& 6=14(5) = 100>1(10) = 4(0) ? ?(10) = 4⑸? W = 100 x 3 = 300.a(5)4.分别对以下两种总量函数计算订和讪:(1) A(t) = 100 + 5t; (2) A(t) = 100(1 + 0.1⼫?解：(1)_ 4(5) - 4(4)5 _ 4(4)5⼆⾯-.17% . 4(10)-4(9)210 =—4(9)—5=—^ 3.45%145⑵_ 4(5) - 4(4)5 - 4⑷_ 100(1 + 0.1)5 - 100(1 + 0.1)4 = 100(1+ 0.1)4=10%. 4(10) —4(9)⽫=_ 100(1+ O.1)10-100(1+ 0.1)9 = 100(1 + 0.1)9=10%5?设4(4) = 1000, i n = O.Oln.试计算4(7)。

北大版金融数学引论第二章答案

如果它们前十年每年底存款1000元，后十年每年底存款1000+X 元，年利率7%。

计算X 。

解：S = 1000s 20¬p7%+Xs 10¬p7%X =50000 −1000s 20¬p 7%s 10¬p7%= 651.722．价值10,000元的新车。

购买者计划分期付款方式：每月底还250元，期限4年。

月结算名利率18%。

计算首次付款金额。

解：设首次付款为X ，则有10000 = X + 250a 48¬p1.5%解得X = 1489.363．设有n 年期期末年金，其中年金金额为n ，实利率i =1。

试计算该年金的现值。

解：P V = na¬n pi1 − v nn= n 1n=(n + 1)nn 2− n n+2 (n + 1)n4．已知：a¬n p= X ，a 2¬n p= Y。

试用X 和Y 表示d 。

解： a 2¬n p= a¬n p+ a¬np (1 − d )n则Y − X1d = 1 − ( X ) n5．已知：a¬7p= 5.58238, a 11¬p= 7.88687, a 18¬p= 10.82760。

计算i 。

解：a 18¬p = a¬7p + a 11¬p v 7解得6.证明： 11−v10=i = 6.0%s。

国际金融专题答案北大

国际金融专题答案北大《国际金融专题》复习题答案（供参考）――李妍婷（整理）第一章第二章导论 ...................................................... ......................................................... ..................... 1 国际收支基础 ...................................................... ......................................................... . (1)1. 国际收支平衡表的记账原则和记帐方法。

（必考）..................................................... .... 1 2. 国际收支平衡表的局部差额分析。

.................................................... ................................ 4 3. 金本位下、固定汇率纸币本位下、浮动汇率下国际收支的自我调节机制（重点）. 6 4. 概念： ............................................................................................................. . (7)（1）（2）（3）（4）（5）（6）第三章国际收支平衡表 ...................................................... ............................................ 7 自主性交易和补偿性交易 ...................................................... ............................ 7 赤字和盈余 ...................................................... .. (7)全面性控制与选择性控制 ...................................................... ............................ 8 冲销政策 ...................................................... .........................................................8 外汇缓冲政策 ...................................................... (9)国际收支理论 ...................................................... ......................................................... . (9)1. M－L条件的推导及其含义（重点）..................................................... ............................ 9 2. 弹性论对货币贬值三个阶段和J曲线的论述（重点） (10)3. 货币论中不同汇率制度下收入、价格和货币扩张对国际收支的影响（重点）....... 11 4. 用货币论的基本模型比较固定汇率制度和浮动汇率制度的优劣（重点）............... 15 5. 名词解释： .................................................... ......................................................... (15)（1）贸易条件 ...................................................... . (15)经济学院07金融 I（2）（3）（4）（5）第四章贬值的价格效应与数量效应 ...................................................... ..................... 16 贬值的消费者和生产者反应时滞（重点） (16)外汇市场操作 ...................................................... .............................................. 17 冲销性外汇操作 ...................................................... (17)外汇与外汇基础 ...................................................... .......................................................171. 外汇的基本特征 ...................................................... ......................................................... .... 17 2. 汇率的标价方法和套算汇率的方法（重点）..................................................... ............ 18 3. 通过掉期率来表示远期汇率的方法（重点）..................................................... ............ 20 4. 金本位下通过黄金输送点保持固定汇率的作用机制（重点）.................................... 21 5. Walras拍卖者和造市者的不同，外汇市场均衡价格的产生机制 .............................. 22 6. 几个概念： .................................................... ......................................................... (23)（1）（2）（3）（4）（5）逆风行事原则 ...................................................... .............................................. 23 货币替换 ...................................................... .......................................................23 联合干预 ...................................................... .......................................................24 肮脏浮动 ...................................................... .......................................................24 单向投机的自我实现 ...................................................... . (24)7. 描述固定汇率制的运行机制 ...................................................... ........................................ 24 第五章汇率理论 ...................................................... (26)1. 一价定率和商品套购的过程与结果 ...................................................... ............................ 26 2. 绝对购买力平价和相对购买力平价的含义和计算（重点）........................................ 27 3. 抛补套利和非抛补套利的含义 ...................................................... .................................... 27 4. 利率平价公式的推导过程和含义（重点）..................................................... . (28)经济学院07金融 II5. 用预期收益率曲线分析利率变动对均衡汇率的影响 .....................................................30 6. 比较汇率的弹性价格货币模型与粘性价格模型的异同。

《金融学》第二章答案金融系统

CHAPTER 2THE FINANCIAL S YS TEMObjectives∙To provide a conceptual framework for understanding how the financial system works and how it changes over time.∙To understand the meaning and determinants of rates of return on different classes of assets.Outline2.1 What Is the Financial System?2.2 The Flow of Funds2.3 The Functional Perspective2.4 Financial Innovation and the “Invisible Hand”2.5 Financial Markets2.6 Financial Market Rates2.7 Financial Intermediaries2.8 Financial Infrastructure and Regulation2.9 Governmental and Quasi-Governmental OrganizationsSummary∙The financial system is the set of markets and intermediaries used by households, firms, and governments to implement their financial decisions. It includes the markets for stocks, bonds, and other securities, as well as financial intermediaries such as banks and insurance companies.∙Funds flow through the financial system from entities that have a surplus of funds to those that have a deficit.Often these fund flows take place through a financial intermediary.∙There are six core functions performed by the financial system:1.To provide ways to transfer economic resources through time, across borders, and among industries.2.To provide ways of managing risk.3.To provide ways of clearing and settling payments to facilitate trade.4.To provide a mechanism for the pooling of resources and for the subdividing of shares in variousenterprises.5.To provide price information to help coordinate decentralized decision-making in various sectors of theeconomy.6.To provide ways of dealing with the incentive problems created when one party to a transaction hasinformation that the other party does not or when one party acts as agent for another.∙The fundamental economic force behind financial innovation is competition, which generally leads to improvements in the way financial functions are performed. The basic types of financial assets traded in markets are debt, equity, and derivatives.∙Debt instruments are issued by anyone who borrows money—firms, governments, and households.∙Equity is the claim of the owners of a firm. Equity securities issued by corporations are called common stocks.∙Derivatives are financial instruments such as options and futures contracts that derive their value from the prices of one or more other assets.∙An interest rate is a promised rate of return, and there are as many different interest rates as there are distinct kinds of borrowing and lending. Interest rates vary depending on the unit of account, the maturity, and the default risk of the credit instrument. The nominal interest rate is the promised amount of money you receive per unit you lend.∙The real rate of return is defined as the nominal interest rate you earn corrected for the change in the purchasing power of money. For example, if you earn a nominal interest rate of 8% per year and the rate of price inflation is also 8% per year, then the real rate of return is zero.∙There are four main factors that determine rates of return in a market economy:∙the productivity of capital goods—expected rates of return on mines, dams, roads, bridges, factories, machinery, and inventories,∙the degree of uncertainty regarding the productivity of capital goods,∙time preferences of people—the preference of people for consumption now versus consumption in the future, and∙risk aversion—the amount people are willing to give up in order to reduce their exposure to risk.∙Indexing is an investment strategy that seeks to match the returns of a specified stock market index.∙Financial intermediaries are firms whose primary business is to provide customers with financial products that cannot be obtained more efficiently by transacting directly in securities markets. A mong the main types of intermediaries are banks, investment companies, and insurance companies. Their products include checking accounts, loans, mortgages, mutual funds, and a wide range of insurance contracts.Solutions to Problems at End of Chapter1. Do you agree with Adam Smith’s view that society can rely more on the “invisible hand” than on government to promote economic pros perity?Student answers will vary of course.SAMPLE ANSWER:The communist system is the exact opposite of Adam Smith’s invisible hand. And of course we have recently seen the downfall of many of the communist countries around the world. In the communist world, it was believed that government could make better decisions promoting economic prosperity than individuals could. Clearly this system failed to promote economic prosperity. It seems that Adam Smith’s view was that competitive market systems as a whole (rather than government) could best allocate resources to promote economic prosperity. However, a completely unfettered capitalist society such as in the late 1800s in the Western world may n ot have been the perfect system either as the invisible hand helped the “rich get richer” while the poor and needy had no formal assistance. This outraged the moral fabric of society and government programs were eventually set up to formally address thisi ssue of general welfare and “fairness”.2. How does the financial system contribute to economic security and prosperity in a capitalist society?In a capitalist society, it is the price system which helps make capital resource decisions. Capital flows to those operations which can employ it to earn the highest rate of return. This therefore allocates capital to its most productive use, thereby enhancing society’s economic prosperity. In addition, the financial system has markets and intermediaries which transfer risks from those who are least willing to bear it to those who are most willing to bear it. This benefits society as a whole without costing it anything. In addition, by allowing individuals to reduce or eliminate risks, it fosters an atmosphere of undertaking business ventures which also benefits society.3. Give an example of how each of the six functions of the financial system are performed more efficiently today than they were in the time of Adam Smith (1776).Clearing and settling payments:In Adam Smith’s day, just as today there was paper and coin currency. However, due to technological innovations (primarily the computer) today there are many additional forms of payment settlement such as personal checks, credit cards, debit cards and electronic transfer of funds. In addition, certain credit cards and traveler’s checks are accepted everywhere in the world making currency exchange a relic of the past. Pooling resources and subdividing shares:In Adam Smith’s day, most businesses were s mall and were financed by sole proprietorships. Therefore the need to pool resources to finance large investments was not as prevalent or as important as it is today. Again, the technological revolution of computers and telephones allow for global capital marke ts to efficiently finance today’s much larger businesses. Today these companies can access huge pools of money around the world and find the cheapest source of financing for large scale projects.Transfer economic resources: Today there is a worldwide financial system which facilitates the transfer of resources and risk from one individual to another and from one point in time to another. In Adam Smith’s day, although there were financial markets which played a limited role, they were localized, small and much less efficient and innovative than they are today.Managing risk: Of course during Adam Smith’s day individuals and businesses faced many of the same risks they do today (risk of property damage, risk of financial loss, risk of crop failure etc.) Ho wever, there were limited means to offset this risk. There were some insurance companies in place at that time, however, they concentrated on managing business risk rather than personal risk and certainly there was not the same type of insurance. A good ex ample is that in Adam Smith’s day, there was no unemployment insurance. In Adam Smith’s day, there was very little a farmer could do about reducing his risk of crop failure or lower crop prices. Today there are a vast number of markets and securities which can be used to offset individual and business risk as well as a huge network of insurance companies whose role is to transfer risk from those who want to reduce risk to those who want to take on more risk.Price information: During Adam Smith’s day, info rmation traveled slowly. Of course, there were no phones, televisions or radios. News traveled by newspaper and by the mail. Today, information travels around the worldinstantaneously. Due primarily to the growth and innovation in computer and telephone t echnology, information about security prices and performance is known at virtually the same time everywhere around the world.Incentive problems: As discussed above, today’s financial system is large, innovative and global. In Adam Smith’s day, while there were problems of moral hazard and adverse selection (but less of a principal-agent problem) there was not the same financial system and sophistication to deal with these problems as there is today.4. How does a competitive stock market accomplish the result that Adam Smith describes? Should the stock market be regulated? How and why?Student answers will vary.SAMPLE ANSWER:Adam Smith talked about free and competitive markets as a system which allocates capital to its most productive use and greatest value. In a competitive stock market, prices are set through supply and demand. Those companies returning the highest return will be rewarded with the highest prices (or cheapest source of financing). Those companies which are under performing will not be allocated as much capital because they are not as productive. Because the universe of possible investments is huge and because it is at times difficult for investors to discern which companies are the most productive employers of capital, regulation shou ld be required to make sure relevant and standardized information is disseminated to potential investors. This would include regulation on disclosure and also insider trading and stock manipulation. However other forms of market regulation are perhaps not so important from a market efficiency point of view and may even impede society’s overall financial welfare.5. Would you be able to get a student loan without someone else offering to guarantee it?Since most students do not have any earning power (yet) or source of savings or other capital, it is doubtful any intermediary would take that credit risk at any reasonable interest rate.6. Give an example of a new business that would not be able to get financing if insurance against risk were not available.EXAMPLES:∙Chemical company∙Child safety products company∙Airline∙Bank∙Hospital∙Environmental consulting∙Hazardous waste disposal7. Suppose you invest in a real-estate development deal. The total investment is $100,000. You invest $20,000 of your own money and borrow the other $80,000 from the bank. Who bears the risk of this venture and why?The $20,000 of my own money is considered the equity capital and the $80,000 is debt financing. In general it is the equity investors who absorb the primary risk of business failure. This is because if the business goes bankrupt, I will unlikely get any or my money back as the debt holders get paid back before I do. However, the debt holder also faces some risk that it will not even get back all its principal and interest. So lenders do share some of the business risk along with the equity investors.8. You are living in the United States and are thinking of traveling to Germany 6 months from now. You can purchase an option to buy marks now at a fixed rate of $0.75 per mark 6 months from now. How is the option like an insurance policy?An option means you have a choice. In this example you can choose to buy the marks at $0.75 in 6 months but you do not have to. You will only buy the marks at this price if it is cheaper for you to do so (if the spot market at that time is higher). Therefore, like an insurance policy you are protected against a potential loss. You know that the maximum price you will have to pay is $0.75 per mark and that you are protected against any higher price. Presumably you will have to pay something for the price of that option and that can be equated to an insurance premium.9. Give an example of how the problem of moral hazard might prevent you from getting financing for something you want to do. Can you think of a way of overcoming this problem?SAMPLE ANSWER:Suppose I want to start a biotechnology business and I need a lot of financing. The trouble is, I do not want to disclose my technology secrets to potential equity and debt investors. I will have great difficulty raising financing. But I could do the following: At a minimum, I could require all potential lenders and investors to sign agreements saying they will not disclose any of my secrets. Secondly, I could share some of my equity with potential lenders (equity-kickers) and investors (stock and stock options). At least that way they will not be motivated to disclose my secrets to others. Finally, if I decided I did not want to share secrets, I could give collateral in my new plant to the debt lenders and that might make them more comfortable with the issue of moral hazard.10. Give an example of how the problem of adverse selection might prevent you from getting financing for something you want to do. Can you think of a way of overcoming this problem?SAMPLE ANSWER:Suppose I want to start a car leasing business. Initially my plan was to purchase several automobiles and lease them out at attractive annual rates. However, potential lenders were worried that my business would attract individuals who drive great distances each year. Rather than buy their own car and lose significant value, they would lease my cars and take a new one each year. I would not be able to obtain financing for this business until I instituted annual mileage restrictions. This alteration in the business plan was enough to make the lenders comfortable with the potential problem of adverse selection.11. Give an example of how the principal-agent problem might prevent you from getting financing for something you want to do. Can you think of a way of overcoming this problem?SAMPLE ANSWER:Suppose you want to start a personal care products company. However, you have the idea for the business, but you do not want to actually run the business. To do that you have hired an executive from a competitor. He will own no equity in the business but will be paid a salary of $100,000 to start up the business.Trouble with this example is that the executive you have hired has little incentive to make the business really work other than his salary (which presumably he could earn at many different companies). What if this executive is really a spy? It may be difficult to get financing for this venture. The way to solve the problem is if you the owner decide to run the business (you certainly are motivated for it do well) or at a minimum, grant your new employee stock or stock options in the business.12. Why is it that a country’s postage stamps are not as good a medium of exchange as its paper currency? Postage stamps would be much easier to copy (to counterfeit) than paper currency which has intricate designs and is made of special fibers (not easily duplicated). Secondly, postage stamps would not be as durable as paper currency and because of their other use, could easily stick to other items! Finally, because postage stamps are used for another purpose, one might run out of them and have to make a special trip to the post office to get more. Of course, the post office is not as convenient as an ATM machine for getting a new supply of currency.13. Who is hurt if I issue counterfeit U.S. dollars and use them to purchase valuable goods and services?If this were done in great size, everyone would be hurt through the inflation that would result in the increased money supply. However, if done in a s mall amount, the individuals accepting the currency are taking on the risk (without knowing it) that the dollars will not be accepted by others as a medium of exchange.14. Some say the only criterion to use in predicting what will serve as money in the future is the real resource cost of producing it, including the transaction costs of verifying its authenticity. According to this criterion what do you think will be the money of the future?SAMPLE ANSWER:Payments via electronic transfer may become the medium of choice. It is a very cheap way to create currency. The biggest challenge will be to create security systems that do not allow for tampering and fraud. Once this is done and once most individuals and retail establishments have access to the system (through bank accounts and linking computer systems) then this should become the “currency” of choice.15. Should all governments issue debt that is indexed to their domestic price level? Is there a moral hazard problem that citizens face with regard to their public officials when government debt is fixed in units of the domestic currency?The answer is that all governments should issue debt that is indexed to their domestic price level. This is due to the fact that if debts are not indexed to the domestic price level, governments have the incentive to print money to repay those debts, thereby increasing domestic inflation which negatively impacts all of society.16. Describe your country’s system for financing higher education. Wh at are the roles played by households, voluntary non-profit organizations, businesses and government?SAMPLE ANSWER:In the United States, the vast majority of higher education is paid for by individuals through savings. These sums can be supplemented in whole or in part by government-guaranteed loans and through student loans and scholarships provided by universities themselves as well as by private foundations such as those provided by the Fulbright scholarship.17. Describe your country’s system for fin ancing residential housing. What are the roles played by households, businesses and government?SAMPLE ANSWER:In the United States individuals and individual borrowings from savings and loans, commercial banks and mortgage lending companies finance the vast majority of residential housing through individual equity savings. The government guarantees a certain amount of low income mortgages and local governments finance some low-income housing. Businesses play a role through the lending business as well as through the financial markets which provide liquidity for portfolios of certain standardized mortgages.18. Describe your country’s system for financing new enterprises. What are the roles played by households, businesses and government?SAMPLE ANSWER:In the United States, the vast majority of new enterprises is financed through individual savings and through initial public offerings made to the general public. These sources of financing are augmented by established firms which spend research and development (R&D) dollars developing new products and businesses and by venture capital institutions which also provide start-up financing.19. Describe your country’s system for financing medical research. What are the roles played by voluntary non-profit organizations, businesses and government?SAMPLE ANSWER:In the United States, medical research is financed both by non-profit organizations (such as universities and medical facilities as well as organizations such as the American Heart Association) as well as by businesses such as Merck, Johnson & Johnson and Genentech. The government is involved in research grants, primarily to universities.20. Assume there are only two stocks traded in the stock market, and you are trying to construct an index to show what has happened to stock prices. Let us say that in the base year the prices were $20 per share for stock 1 with 100 million shares outstanding and $10 for stock 2 with 50 million shares outstanding. A year later, the prices are $30 per share for stock 1 and $2 per share for stock 2. Using the two different methods explained in the chapter, compute stock indexes showing what has happened to the overall stock market. Which of the two methods do you prefer and why? (See appendix that follows.)DJI-Type Index = Average of Current Prices/Average of Base Prices * 100 = 106.67S&P-Type Index = (Weight of Stock 1 * Current Price of Stock 1 / Base Price of Stock 1 + Weight of Stock 2 * Current Price of Stock 2/Base Price of Stock 2) * 100 = 124The S&P-Type Index accurately reflects what has happened to the total market value of all stocks.。

《金融数学》(第二版)习题参考答案(修订版)

1 i
(an−1
− vnan−1
+1− vn)
=
1 i
(1
−
v
n
)(a n
−1
+ 1)
=a n
⋅a n
3.8
1000
×
1
−
⎛ ⎜⎝
1.1 1.05
⎞10 ⎟⎠
= 11846.66
0.05 − 0.10
10 − a
3.9 300a + 50(Da) = 300a + 50
10 0.08 = 6250 − 325A
故最后一次付款的时间是 23 年末，付款额为 1176.23 元。
2.16 100a = 4495.5038 = 6000vk ⇒ vk = 0.7493 ⇒ k = 29 60
2.17
1− vn
a=
= x,
a = 1− v2n = y
n
i
2n
i
⇒ 1− (1− ix)2 i
=
y
⇒i
=
2x + x2
第三部分是自55年开始支付5次每次支付2x故有050545500001051053278516由已知115045869228001001由过去法第2期后未偿还本金金额为10001018692288453852次支付的本金金额为001784689由将来法第4期后未偿还本金金额为次支付的利息金额为0015138212517第69期还款额中本金金额为3606929269rvrv故由已知292292094473rv和70期偿还的本金金额比为944186970同样解得01196518由已知前10次付款等于应付利息故十年末的未偿还贷款余额仍为1000第11至20次付款等于应付利息的两倍即本金偿还值等于应付利息值有11101110111011101211101010201000809209209209209210004343885后10期每期付款等于x故206474008104343885519分别用将来法计算两种偿还方式在第5次付款之后的未偿还本金有10005100050051000800kvia487914

金融数学引论答案第5—7章北京大学出版

并说明如果收益率下调10%，债券价格上涨的百分比。

解：(1)记P为买价，则有价值方程:P1(1 + 10%)10 = 1000P2(1 + 9%)10 = 1000解得:P1 = 385.54元P2 = 422.41元(2)收益率下降后P1(1 + 10% ×90%)10 = 1000P2(1 + 9% ×90%)10 = 1000解得:P1 = 422.41元，上涨百分比:9.56%; P2 = 458.93元，上涨百分比:8.65%。

2. 已知26周的短期国债的发行价格为9600元，到期兑现10,000元。

1〕按短期国债计算天数的典型方法计算贴现率；2〕假定投资期恰为半年，计算年收益率。

解：(1)由短期国债的定价公式10000(1 −Y dt360) = 9600解得：Y d = 7.91%(2)由定义设年换算收益率为i，则：9600(1 + i)12 = 10000解得：i = 8.51%3. 短期国债的贴现率均为8%，计算52 周国债与13 周短期国债的年利率之比。

52周实际天数已经超过360，如何处理；年利率之比是指等价年利率之比还是贴现率的比。

4. 某10年期面值为100元的债券半年名息率10%，到期兑现105元，如果收益率为半年换算8%，计算债券的买价。

1) ∂P∂i , ∂P∂n和∂P∂g2) ∂n∂P和∂n∂P解：(1.1)由基本公式对i求导：∂P∂i= Fr(Da)n p i −nP(n + 1, i) < 0解释：债券的买价随着年限的增加而递减。

金融数学课后复习题答案 2

第一章习题答案1. 设总量函数为A(t) = t2 + 2t + 3 。

试计算累积函数a(t) 和第n 个时段的利息In 。

解: 把t = 0 代入得A(0) = 3 于是:a(t) =A(t)A(0)=t2 + 2t + 33In = A(n) − A(n −1)= (n2 + 2n + 3) −((n −1)2 + 2(n −1) + 3))= 2n + 12. 对以下两种情况计算从t 时刻到n(t < n) 时刻的利息: (1)Ir(0 < r <n); (2)Ir = 2r(0 < r < n).解:(1)I = A(n) − A(t)= In + In¡ 1 + ・・・+ It+1=n(n + 1)2− t(t + 1)2(2)I = A(n) − A(t)=Σnk=t+1Ik =Σnk=t+1Ik= 2n+1 −2t+13. 已知累积函数的形式为: a(t) = at2 + b 。

若0 时刻投入的100 元累积到3 时刻为172 元，试计算：5 时刻投入的100 元在10 时刻的终值。

第1 页解: 由题意得a(0) = 1, a(3) =A(3)A(0)= 1.72⇒ a = 0.08, b = 1∴A(5) = 100A(10) = A(0) ・ a(10) = A(5) ・ a(10)a(5)= 100 ×3 = 300.4. 分别对以下两种总量函数计算i5 和i10 :(1) A(t) = 100 + 5t; (2) A(t) = 100(1 + 0.1)t.解：(1)i5 =A(5) − A(4)A(4)=5120≈4.17%i10 =A(10) − A(9)A(9)=5145≈3.45%(2)i5 =A(5) − A(4)A(4)=100(1 + 0.1)5 −100(1 + 0.1)4100(1 + 0.1)4= 10%i10 =A(10) − A(9)A(9)=100(1 + 0.1)10 −100(1 + 0.1)9100(1 + 0.1)9= 10%第2 页5.设A(4) = 1000, in = 0.01n. 试计算A(7) 。

《金融数学》(第二版)习题参考答案(修订版)

δ0.5 = a' (0.5) / a (0.5) =（0.08*0.5+0.03）/(1+2.5%)=0.06829
∫ 1.15
A(3) = 100⋅ exp⎜⎝⎛⎜
3
t2
0
/ 100dt⎞⎠⎟⎟+
X
= 109.42 +
X
∫ A(6) = (109.42 + X )⋅exp⎛⎜⎜⎝
6t2
3
/ 100dt⎞⎠⎟⎟
第三部分是自55年开始支付5次每次支付2x故有050545500001051053278516由已知115045869228001001由过去法第2期后未偿还本金金额为10001018692288453852次支付的本金金额为001784689由将来法第4期后未偿还本金金额为次支付的利息金额为0015138212517第69期还款额中本金金额为3606929269rvrv故由已知292292094473rv和70期偿还的本金金额比为944186970同样解得01196518由已知前10次付款等于应付利息故十年末的未偿还贷款余额仍为1000第11至20次付款等于应付利息的两倍即本金偿还值等于应付利息值有11101110111011101211101010201000809209209209209210004343885后10期每期付款等于x故206474008104343885519分别用将来法计算两种偿还方式在第5次付款之后的未偿还本金有10005100050051000800kvia487914
200a ×(1+ 0.5%)123 = 33873 123 0.5%
200a ×(1+ 0.5%)70 = 26005 123 0.5%

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