chapter2金融工程
金融工程2
案例续
长期资本管理公司以“不同市场证券间不合理价差生灭自 然性”为基础，制定了“通过电脑精密计算，发现不正常 市场价格差，资金杠杆放大，入市图利”的投资策略。 舒尔茨和默顿将金融市场历史交易资料，已有的市场理论、 学术研究报告和市场信息有机结合在一起，形成了一套较 完整的电脑数学自动投资模型。他们利用计算机处理大量 历史数据，通过连续而精密的计算得到两种不同金融工具 间的正常历史价格差，然后结合市场信息分析它们之间的 最新价格差。如果两者出现偏差，并且该偏差正在放大， 电脑立即建立起庞大的债券和衍生工具组合，大举套利入 市投资；经过市场一段时间调节，放大的偏差会自动恢复 到正常轨迹上，此时电脑指令平仓离场，获取偏差的差值。
金融工程
福建师范大学经济学院 张业圳
第一节 金融工程的作用
提供风险管理的工具与技术 投机和套利机会的发掘 公司重组安排与财务配置 避税策略和税务筹划
一、提供风险管理的工具与技术
风险管理在金融工程中居于核心地位。 风险即不确定性 1、用不确定性来代替风险； 2、替换掉与己不利的风险，保留有利风险。 3、分散风险 案例：最初出现于20世纪70年代初的美国住房 抵押贷款市场资产证券化方案的实施
案例：ESL 投资基金收购K-Mart
K-Mart经营不善债务累累﹐二十亿美金的债务 无法偿还﹐导致这个百 年老店被迫进入破产保 护。2003年5月5日是K-Mart可以走出破产法庭 最后期限﹐就在此生死存亡关头﹐当时名不见 经传的康州40岁投资人爱得华兰博(Edward Lampert) 的ESL 投资基金 公司成功地将二十 亿美金的债务折价买下(具体金额是保密的﹐ 业内灵通人士估计在二亿五至五亿之间)﹐然 后投资三亿五定向增发给ESL﹐使得他成为走 出破产后K-Mart公司的69%大股东。
第二章 金融工程基本原理《金融工程》PPT课件
相同，但它们的成本（价格）不同，这时市场存在套利机 会。 ➢ （2）如果存在两个相同成本（价格）的组合，第一个组合 在所有状态下的收益都不低于第二个组合，而且至少存在 一种状态，在此状态下第一个组合的收益大于第二个组合 ，这时市场存在套利机会。 ➢ （3）如果一个组合的构建成本为0，但在所有状态下这个 组合的收益都不小于0，而且至少存在一种状态，在此状态 下这个组合的收益大于0，则市场存在套利机会。
90
无风险资产：
1 1
1
144 108 81
1 1 1
B：
PB
128
PB1 110
PB2
101
16
无套利定价原理的应用
复制策略的确定用倒推法：
（1）在t=0.5时刻：
当PA＝120时：144x y 128
x 0.5
108x y 110
y 56
PB1 120 0.5 56 116
当PA＝90时：
0 -1个B：-101
合计：
0
1/3A： 27
存款： 74
020
第二节 风险中性定价方法
一、风险中性的概念 ➢ 公平博彩 ➢ 如果一个参加者，他刚好可以接受这样一个统计意
义上的公平博彩，他就是风险中性的 ➢ 风险中性投资者投资于风险证券，不需要风险补偿
，只要收益率等于无风险利率就可以了 ➢ 如果市场上的投资者都是风险中性的，则任何一个
持有证券B空头 持有动态复制策略多头
-1个B：-128 0.5A： 72 存款： 56
卖出B： 110元 买入0.4A：-40元 存款68元：-68 合计： 2
02 金融工程的基本理论
市场交易中的异象
⑴ 交易动机与交易策略——传统金融理论认为，在假设和市场预期均衡状态 下，交易者都会持有一个由市场组合和无风险证券构成的投资组合，其持 有的证券比例取决于交易者的风险承受能力。但统计数据显示，美国纽约 证券交易所市场中一天成交7亿股，投资者的交易行为呈现出“非理性”的 过度交易倾向。 ⑵ 分散不足与随机分散——投资者持有的证券数量很少，显著少于标准的投 资组合理论所推荐的构成分散化投资组合的证券数量，而且投资者在构建 投资组合时采用随机方式选择证券。
2 1 2 1
假设：资产2为无 E ( rp ) = ω1 E ( r1 ) + ( 1-ω1 )rf = rf -ω1 ( E ( r1 )-rf ) 风险资产：
σ p = ω1σ1
ρ≤1
设
r = r1 -tr2
= E[(r1 - r1 ) - t(r2 - r2 )] 2
2 2 = σ1 - 2 tσ 12 + t 2 σ 2 ≥0
1. 有效市场假设的含义 2. 有效市场假设下的投资管理 3. 有效市场理论的检验 4. 与有效市场理论相悖的异象
有效市场假设的含义
1970年，法马采用公平博弈模型来描述有效市场假设，公平博弈模型的假 设条件是：在任一时点，有关某种证券的所有信息都已经充分反映在股票 价格中。模型对信息的处理是非常详尽的，目的是达到“充分反映”的要 求，从而验证了股票价格或收益率序列在统计上不具有“记忆性”，所以 投资者无法根据历史的价格来预测其未来的走势。
金融工程 Financial Engineering
第2章 金融工程的基本理论
1 2 3 4
• 有效市场理论
• 资产组合理论
• 资本资产定价模型 • 因素模型和套利定价模型
金融工程Chapter2
2
金融远期合约（Forward Contracts）是指双方约定在未 来的某一确定时间，按确定的价格买卖一定数量的某种金 融资产的合约。在合约中，未来将买入标的物的一方称为 多方（Long Position），而在未来将卖出标的物的一方称 为空方（Short Position）。
23
❖ 特定期货合约的合约规模、交割日期和交割地点等都 是标准化的，在合约上均有明确规定，无须双方再商 定，价格是期货合约的唯一变量。
❖ 一般来说，常见的标准期货合约条款包括： (1)交易单位。交易所对每个期货产品都规定了统 一的数量和数量单位，统称“交易单位”（Trade Unit）或“合约规模”（Contract Size）。不同交 易所、不同期货品种的交易单位规定各不相同。
17
与远期合约的分类相似，根据标的资产不同， 常见的金融期货主要可分为股票指数期货、外汇期 货和利率期货等。 -股票指数期货是指以特定股票指数为标的资产的期 货合约，S&P500股指期货合约就是典型代表。 -外汇期货则以货币作为标的资产，如美元、德国马 克、法国法郎、英镑、日元、澳元和加元等。 -利率期货是指标的资产价格依赖于利率水平的期货 合约，如欧洲美元期货和长期国债期货等。
Copyright© Zheng Zhenlong & Chen Rong, 2008
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3．远期股票合约 远期股票合约（Equity Forwards）是指在将来某一特 定日期按特定价格交付一定数量单只股票或一揽子 股票的协议。远期股票合约在世界上出现时间不长， 总交易规模也不大。
Copyright© Zheng Zhenlong & Chen Rong, 2008
金融工程2(金融市场)共36页
缅甸玉石的启示：新信息
在缅甸开采玉石矿的市场上，摆放着各种未 经过任何雕琢的矿石。这些矿石中有可能包 含有大量的翡翠，也可能只有很少一点翡翠。 买卖双方其实都不知道这些矿石中究竟含有 玉多 以 现石便 玉少？请使 石翡得大之 有翠到家露可。新讨出能买信论更含主息：多有可你之有高以是后关成选否，成色择有对色的打必你的翡磨要有信 翠和去好息 ，擦打处， 那拭磨吗一 么玉一？旦 卖石块发 方， 就会相应提高价格，反之降价。从这个例子 中，我们可以得出两点重要的发现：(1) 信 息越多的地方，不确定性就越少，越容易形 成双方都接受的稳定价格。(2) 市场价格的 变动是由新出现的信息推动的，因为新信息 改变了人们对某资产未来价值的预期。
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第二章 金融市场 -Financial Market
我们需要了解金融市场的目的
金融市场提供什么样的信息？ 如何利用金融市场的信息作正确的决定？ 资本性资产定价如何在金融市场上定价？ 企业和金融市场之间存在什么关系？ 市场对于金融三要素的反应。
课堂讨论—《黑天鹅》作者名言选读
例2-1:第四个和尚买水喝 例2-3:经济大萧条时期为什么会有人销毁高炉? 例2-4:安然公司垄断现货市场为什么还会破产? 例2-5:国家储备局的失误
思考:是什么促成了金融市场价格波动?
有效金融市场假设
什么是有效金融市场呢？
一个简单的定义就是：在一个有效金融市场 上，以当时的市场价格简单地买入或者卖出 一项金融资产，并不能够使投资人实现任何 套利的利润（该定义引自Richard A. Brealey和
《金融工程》新第二版习题答案郑振龙
《⾦融⼯程》新第⼆版习题答案郑振龙《⾦融⼯程》课后题答案第⼆章1、按照式⼦：（1＋8%）美元＝1．8×（1＋4%）马克，得到1美元＝1．7333马克。
2、设远期利率为i，根据（1＋9．5%）×（1＋i）＝1＋9．875%，i＝9．785%．3、存在套利机会，其步骤为：（1）以6%的利率借⼊1655万美元，期限6个⽉；（2）按市场汇率将1655万美元换成1000万英镑；（3）将1000万英镑以8%的利率贷出，期限6个⽉；（4）按1．6600美元/英镑的远期汇率卖出1037．5万英镑；（5）6个⽉后收到英镑贷款本息1040．8万英镑（1000e0．08×0．5），剩余3．3万英镑；（6）⽤1037．5万元英镑换回1722．3万美元（1037．5×1．66）；（7）⽤1715．7美元（1665 e0．06×0．5）归还贷款本息，剩余6．6万美元；（8）套利盈余＝6．6万美元＋3．3万英镑。
4、考虑这样的证券组合：购买⼀个看涨期权并卖出Δ股股票。
如果股票价格上涨到42元，组合价值是42Δ－3；如果股票价格下降到38元，组合价值是38Δ。
若两者相等，则42Δ－3＝38Δ，Δ＝075。
可以算出⼀个⽉后⽆论股票价格是多少，组合的价值都是28．5，今天的价值⼀定是28．5的现值，即2 8．31＝28．5 e－0．08×0．08333。
即－f＋40Δ＝28．31，f是看涨期权价格。
f＝1．69。
5、按照风险中性的原则，我们⾸先计算风险中性条件下股票价格向上变动的概率p，它满⾜等式：42p＋38（1－p）＝40e0．08×0．08333，p＝0．5669，期权的价值是：（3×0．5669＋0×0．4331）e－0．0 8×0．08333＝1．69，同题4按照⽆套利定价原则计算的结果相同。
6、考虑这样的组合：卖出⼀个看跌期权并购买Δ股股票。
Assignment for Chapter 2宋逢明金融工程习题
Assignment for Chapter2:Now given the risk-free zero coupon rate as following:Term1 year2 year3 year4 year Risk-free rate 3.25% 3.33% 3.41% 3.60%（1）Question: There is an interest swap: principal 1million, 4 years, fixed interest to floatinterest, change the interest every year. What is the price of the swap?（2）Question: Assume the risk-free zero coupon rate changed one year later. Show in the Risk-free rate 3.40% 3.52% 3.65% 3.74%Currency swap has a remaining life of 15 months. It involves exchanging interest at 14% on 20 million pound for interest at 10% on $30 million once a year. The term structure of interest rates in both the UK and the US is currently flat, and if the swap were negotiated today the interest rates exchanged would be 8% in dollars and 11% in pound. All interest rates are quoted with annual compounding. The current exchange rate (dollars per pound) is 1.65. What is the value of the swap to the party paying pound sterling? What is the value of the swap to the party paying dollars?A financial institution has entered into an interest rate swap with company X. Under the terms of the swap, it receives 10% per annum and pays six-month LIBOR on a principal of $10 million for five years. Payments are made every six months. Suppose that company X defaults on the sixth payment date (end of year three) when the interest rate (with semiannual compounding) is 8% per annum for all maturities. What is the loss to the financial institution? Assume that six-month LIBOR was 9% per annum halfway through year three.4. The term structure is upward sloping. Put the following in order of magnitude:(1) The five-year zero rate.(2) The yield on a five-year coupon-bearing bond.(3) The forward rate corresponding to the period between 5 and 415years in the future. What is the answer to this question when the term structure is downward sloping?5. A $100 million interest rate swap has a remaining life of 10 months. Under the terms of theswap, six-month LIBOR is exchanged for 12% per annum (compounded semiannually). The average of the bid-ask rate being exchanged for six-month LIBOR in swaps of all maturities is currently 10% per annum with continuous compounding. The six-month LIBOR rate was9.6% per annum two months ago. What is the current value of the swap to the party paying floating? What is its value to the party paying fixed?。
(完整版)《金融工程学》各章学习指南
第一章 金融工程概述学习指南1. 主要内容 金融工程是一门融现代金融学、工程方法与信息技术于一体的新兴交叉性学科。
无套利定价与风险中性定价是金融工程具有标志性的分析方法。
尽管历史不长，但金融工程的发展在把金融科学的研究推进到一个新阶段的同时，对金融产业乃至整个经济领域都产生了极其深远的影响.本章主要对金融工程的定义，发展历史以及基本方法进行了介绍2. 学习目标掌握金融工程的定义、根本目的和主要内容;熟悉金融工程产生和发展的背景、金融产品定价的基本分析方法和运用的工具；了解金融工程的主要技术手段、金融工程与风险管理之间的关系3。
本章重点（1）金融工程的定义及主要内容（2） 掌握金融工程的定价原理（绝对定价法和相对定价法,无套利定价原理，风险中性定价法，状态价格定价法)（3） 衍生证券定价的假设4。
本章难点（1) 用积木分析法给金融工程定价（2） 三种定价方法的内在一致性5。
知识结构图6. 学习安排建议本章是整个课程的概论，介绍了有关金融工程的定义、发展历史和背景、基本原理等内容，是今后本课程学习的基础，希望同学们能多花一些时间理解和学习，为后续的学习打好基础。
● 预习教材第一章内容；● 观看视频讲解；● 阅读文字教材;● 完成学习活动和练习，并检查是否掌握相关知识点,否则重新学习相关内容。
● 了解感兴趣的拓展资源。
第二章 远期与期货概述学习指南 1。
主要内容远期是最基本、最古老的衍生产品。
期货则是远期的标准化.在这一章里，我们将了解远期和期货的基础知识，包括定义、主要类型和市场制度等，最后将讨论两者的异同点2. 学习目标掌握远期、期货合约的定义、主要种类;熟悉远期和期货的区别；了解远期和期货的产生和发展、交易机制3。
本章重点(1) 远期、期货的定义和操作（2） 远期、期货的区别4. 本章难点远期和期货的产生和发展、交易机制5. 知识结构图6. 学习安排建议本章主要对远期和期货的基础知识进行介绍，是之后进行定价、套期保值等操作的基础，建议安排1课时的时间进行学习。
金融工程-chapter2共46页
2.1.2 主要金融远期合约种类
• 根据标的资产不同，常见的金融远期合约 包括 1.远期利率协议 2.远期外汇协议 3.远期股票合约
2.1.2 主要金融远期合约种类
• 1．远期利率协议
远期利率协议是买卖双方同意从未来某一商定 的时期开始在某一特定时期内按协议利率借贷一 笔数额确定、以具体货币表示的名义本金的协议。 之所以称为“名义”，是因为借贷双方不必交换 本金，只是在结算日根据协议利率和参考利率之 间的差额以及名义本金额，由交易一方付给另一 方结算金。
• 远期合约并不能保证其投资者未来一定盈 利，但投资者可以通过远期合约获得确定 的未来买卖价格，从而消除了价格风险。
2.1.1 金远期合约的定义
盈亏
盈亏
K 标的资产价 格
K 标的资产价 格
(a) 远期多头的 到期盈亏
(b) 远期空头的 到期盈亏
如果到期标的资产的市场价格高于交割价格K，远期多头就 盈利而空头就会亏损;反之，远期多头就亏损而空头就会盈 利。
远期利率是指现在时刻的将来一定期限的利率。 如14远期利率，即表示1个月之后开始的期限3 个月的远期利率。
2.1.2 主要金融远期合约种类
• 2．远期外汇合约
远期外汇合约是指双方约定在将来某一时间按 约定的远期汇率买卖一定金额的某种外汇的合约。
按照远期的开始时期划分，远期外汇合约又分 为直接远期外汇合约和远期外汇综合协议。
第二章 远期与期货概述
2.1.1 金融远期合约的定义
• 金融远期合约（Forward Contracts）是指 双方约定在未来的某一确定时间，按确定 的价格买卖一定数量的某种金融资产的合 约。在合约中,未来将买入标的物的一方称 为多方（Long Position），而在未来将卖 出标的物的一方称为空方（Short Position）。
金融工程 相关习题及答案
Chapter 1 Market Organization and Structure PRACTICE PROBLEMS FOR CHAPTER 11. Akihiko Takabe has designed a sophisticated forecasting model, which predicts the movements in the overall stock market, in the hope of earning a return in excess of a fair return for the risk involved. He uses the predictions of the model to decide whether to buy, hold, or sell the shares of an index fund that aims to replicate the movements of the stock market. Takabe would best be characterized as a (n):A. hedger.B. investor.C. information-motivated trader.2. James Beach is young and has substantial wealth. A significant proportion of his stock portfolio consists of emerging market stocks that offer relatively high expected returns at the cost of relatively high risk. Beach believes that investment in emerging market stocks is appropriate for him given his ability and willingness to take risk. Which of the following labels most appropriately describes Beach?A. Hedger.B. Investor.C. Information-motivated trader.3. Lisa Smith owns a manufacturing company in the United States. Her company has sold goods to a customer in Brazil and will be paid in Brazilian real (BRL) in three months. Smith is concerned about the possibility of the BRL depreciating more than expected against the U.S. dollar (USD). Therefore, she is planning to sell three-monthfutures contracts on the BRL. The seller of such contracts generally gains when the BRL depreciates against the USD. If Smith were to sell these future contracts, she would most appropriately be described as a (n):A. hedger.B. investor.C. information-motivated trader.4. Which of the following is not a function of the financial system?A. To regulate arbi trageurs’ profits (excess returns).B. To help the economy achieve allocational efficiency.C. To facilitate borrowing by businesses to fund current operations.5. An investor primarily invests in stocks of publicly traded companies. The investor wants to increase the diversification of his portfolio. A friend has recommended investing in real estate properties. The purchase of real estate would best be characterized as a transaction in the:A. derivative investment market.B. traditional investment market.C. alternative investment market.6. A hedge fund holds its excess cash in 90-day commercial paper and negotiable certificates of deposit. The cash management policy of the hedge fund is best described as using:A. capital market instruments.B. money market instruments.C. intermediate-term debt instruments.7. An oil and gas exploration and production company announces that it is offering 30million shares to the public at $45.50 each. This transaction is most likely a sale in the:A. futures market.B. primary market.C. secondary market.8. Consider a mutual fund that invests primarily in fixed-income securities that have been determined to be appropriate given the fund’s investment goal. Which of the following is least likely to be a part of this fund?A. Warrants.B. Commercial paper.C. Repurchase agreements.9. A friend has asked you to explain the differences between open-end andclosed-end funds. Which of the following will you most likely include in your explanation?A. Closed-end funds are unavailable to new investors.B. When investors sell the shares of an open-end fund, they can receive a discount or a premium to the fund’s net asset value.C. When selling shares, investors in an open-end fund sell the shares back to the fund whereas investors in a closed-end fund sell the shares to others in the secondary market.10. The usefulness of a forward contract is limited by some problems. Which of the following is most likely one of those problems?A. Once you have entered into a forward contract, it is difficult to exit from the contract.B. Entering into a forward contract requires the long party to deposit an initialamount with the short party.C. If the price of the underlying asset moves adversely from the perspective of the long party, periodic payments must be made to the short party.11. Tony Harris is planning to start trading in commodities. He has heard about the use of futures contracts on commodities and is learning more about them. Which of the following is Harris least likely to find associated with a futures contract?A. Existence of counterparty risk.B. Standardized contractual terms.C. Payment of an initial margin to enter into a contract.12. A German company that exports machinery is expecting to receive $10 million in three months. The firm converts all its foreign currency receipts into euros. The chief financial officer of the company wishes to lock in a minimum fixed rate for converting the $10 million to euro but also wants to keep the flexibility to use the future spot rate if it is favorable. What hedging transaction is most likely to achieve this objective?A. Selling dollars forward.B. Buying put options on the dollar.C. Selling futures contracts on dollars.13. A book publisher requires substantial quantities of paper. The publisher and a paper producer have entered into an agreement for the publisher to buy and the producer to supply a given quantity of paper four months later at a price agreed upon today. This agreement is a:A. futures contract.B. forward contract.C. commodity swap.14. The Standard & Poor’s Depositary Receipts (SPDRs) is an investment that tracks the S&P 500 stock market index. Purchases and sales of SPDRs during an average trading day are best described as:A. primary market transactions in a pooled investment.B. secondary market transactions in a pooled investment.C. secondary market transactions in an actively managed investment.15. The Standard & Poor’s Depositary Receipts (SPDRs) is an exchange-traded fund in the United States that is designed to track the S&P 500 stock market index. The current price of a share of SPDRs is $113. A trader has just bought call options on shares of SPDRs for a premium of $3 per share. The call options expire in five months and have an exercise price of $120 per share. On the expiration date, the trader will exercise the call options (ignore any transaction costs) if and only if the shares of SPDRs are trading:A. below $120 per share.B. above $120 per share.C. above $123 per share.16. Which of the following statements about exchange-traded funds is most correct?A. Exchange-traded funds are not backed by any assets.B. The investment companies that create exchange-traded funds are financial intermediaries.C. The transaction costs of trading shares of exchange-traded funds are substantially greater than the combined costs of trading the underlying assets of the fund.17. Jason Schmidt works for a hedge fund and he specializes in finding profit opportunities that are the result of inefficiencies in the market for convertiblebonds—bonds that can be converted into a predetermined amount of a company’s common stock. Schmidt tries to find convertibles that are priced inefficiently relative to the underlying stock. The trading strategy involves the simultaneous purchase of the convertible bond and the short sale of the underlying common stock. The above process could best be described as:A. hedging.B. arbitrage.C. securitization.18. Pierre-Louis Robert just purchased a call option on shares of the Michelin Group.A few days ago he wrote a put option on Michelin shares. The call and put options have the same exercise price, expiration date, and number of shares underlying. Considering both positions, Robert’s exposure to the risk of th e stock of the Michelin Group is:A. long.B. short.C. neutral.19. An online brokerage firm has set the minimum margin requirement at 55 percent. What is the maximum leverage ratio associated with a position financed by this minimum margin requirement?A. 1.55.B. 1.82.C. 2.22.20. A trader has purchased 200 shares of a non-dividend-paying firm on margin at a price of $50 per share. The leverage ratio is 2.5. Six months later, the trader sells these shares at $60 per share. Ignoring the interest paid on the borrowed amountand the transaction costs, what was the return to the trader during the six-month period?A. 20 percent.B. 33.33 percent.C. 50 percent.21. Jason Williams purchased 500 shares of a company at $32 per share. The stock was bought on 75 percent margin. One month later, Williams had to pay interest on the amount borrowed at a rate of 2 percent per month. At that time, Williams received a dividend of $0.50 per share. Immediately after that he sold the shares at $28 per share. He paid commissions of $10 on the purchase and $10 on the sale of the stock. What was the rate of return on this investment for the one-month period?A. −12.5 percent.B. –15.4 percent.C. –50.1 percent.22. Caroline Rogers believes the price of Gamma Corp. stock will go down in the near future. She has decided to sell short 200 shares of Gamma Corp. at the current market price of €47. The initial margin requirement is 40 percent. Which of the following is an appropriate statement regarding the margin requirement that Rogers is subject to on this short sale?A. She will need to contribute €3,760 as margin.B. She will need to contribute €5,640 as margin.C. She will only need to leave the proceeds from the short sale as deposit and does not need to contribute any additional funds.23. The current price of a stock is $25 per share. You have $10,000 to invest. You borrow an additional $10,000 from your broker and invest $20,000 in the stock. If themaintenance margin is 30 percent, at what price will a margin call first occur?A. $9.62.B. $17.86.C. $19.71.24. You have placed a sell market-on-open order—a market order that would automatically be submitted at the market’s open tomorrow and would fill at the market price. Your instruction, to sell the shares at the market open, is a(n):A. execution instruction.B. validity instruction.C. clearing instruction.25. A market has the following limit orders standing on its book for a particular stock. The bid and ask sizes are number of shares in hundreds.What is the market?A. 9.73 bid, offered at 10.14.B. 9.81 bid, offered at 10.10.C. 9.95 bid, offered at 10.02.26. Consider the following limit order book for a stock. The bid and ask sizes are number of shares in hundredsA new buy limit order is placed for 300 shares at ¥123.40. This limit order issaid to:A. take the market.B. make the market.C. make a new market.27. Currently, the market in a stock is "$54.62 bid, offered at $54.71." A new sell limit order is placed at $54.62. This limit order is said to:A. take the market.B. make the market.C. make a new market.28. Jim White has sold short 100 shares of Super Stores at a price of$42 per share. He has also simultaneously placed a "good-till-cancelled, stop 50, limit 55 buy" order. Assume that if the stop condition specified by White is satisfied and the order becomes valid, it will get executed. Excluding transaction costs, what is the maximum possible loss that White can have?A. $800.B. $1,300.C. Unlimited.29. You own shares of a company that are currently trading at $30 a share. Your technical analysis of the shares indicates a support level of $27.50. That is, if the price of the shares is going down, it is more likely to stay above this level rather than fall below it. If the price does fall below this level, however, you believe that the price may continue to decline. You have no immediate intent to sell the shares but are concerned about the possibility of a huge loss if the share price declines below the support level. Which of the following types of orders could you place to most appropriately address your concern?A. Short sell order.B. Good-till-cancelled stop sell order.C. Good-till-cancelled stop buy order.30. In an underwritten offering, the risk that the entire issue may not be sold to the public at the stipulated offering price is borne by the:A. issuer.B. investment bank.C. buyers of the part of the issue that is sold.31 . A British company listed on the Alternative Investment Market of the London Stock Exchange, announced the sale of 6,686,665 shares to a small group of qualified investors at £0.025 per share. Which of the following best describesthis sale?A. Shelf registration.B. Private placement.C. Initial public offering.32. A German publicly traded company, to raise new capital, gave its existingshareholders the opportunity to subscribe for new shares. The existing shareholders could purchase two new shares at a subscription price of €4.58 per share for every 15 shares held. This is an example of a(n):A. rights offering.B. private placement.C. initial public offering.33. Consider an order-driven system that allows hidden orders. The following four sell orders on a particular stock are currently in the system's limit order book. Based on the commonly used order precedence hierarchy, which of these orders will have precedence over others?A. Order I (time of arrival of 9:52:01 ).B. Order II (time of arrival of 9:52:08).C. Order III (time of arrival of 9:53:04)34. Zhenhu Li has submitted an immediate-or-cancel buy order for 500 shares of a company at a limit price of CNY 74.25. There are two sell limit orders standing in that stock's order book at that time. One is for 300 shares at a limit price of CNY 74.30 and the other is for 400 shares at a limit price of CNY 74.35. How many shares in Li's order would get cancelled?A. None (the order would remain open but unfilled).B. 200 (300 shares would get filled).C. 500 (there would be no fill).35. A market has the following limit orders standing on its book for a particular stock:Ian submits a day order to sell 1,000 shares, limit £19.83. Assuming that no more buy orders are submitted on that day after Ian submits his order, what would be Ian's average trade price?A. £19.70.B. £19.92.C. £20.05.36. A financial analyst is examining whether a country's financial market is well functioning. She finds that the transaction costs in this market are low and trading volumes are high. She concludes that the market is quite liquid. In such a market:A. traders will find it hard to make use of their information.B. traders will find it easy to trade and their trading will make the market less informationally efficient.C. traders will find it easy to trade and their trading will make the marketmore informationally efficient.37. The government of a country whose financial markets are in an early stage of development has hired you as a consultant on financial market regulation. Your first task is to prepare a list of the objectives of market regulation. Which of the following is least likely to be included in this list of objectives?A. Minimize agency problems in the financial markets.B. Ensure that financial markets are fair and orderly.C. Ensure that investors in the stock market achieve a rate of return that is atleast equal to the risk-free rate of return.Chapter 2 Portfolio Management: An Overview PRACTICE PROBLEMS FOR CHAPTER 21. Investors should use a portfolio approach to:A. reduce risk.B. monitor risk.C. eliminate risk.2. Which of the following is the best reason for an investor to be concerned with the composition of a portfolio?A. Risk reduction.B. Downside risk protection.C. Avoidance of investment disasters.3. With respect to the formation of portfolios, which of the following statements is most accurate?A. Portfolios affect risk less than returns.B. Portfolios affect risk more than returns.C. Portfolios affect risk and returns equally.4. Which of the following institutions will on average have the greatest need for liquidity?A. Banks.B. Investment companies.C. Non-life insurance companies.5. Which of the following institutional investors will most likely have the longest time horizon?A. Defined benefit plan.B. University endowment.C. Life insurance company.6. A defined benefit plan with a large number of retirees is likely to have a high need forA. income.B. liquidity.C. insurance.7. Which of the following institutional investors is most likely to manage investments in mutual funds?A. Insurance companies.B. Investment companies.C. University endowments.8. With respect to the portfolio management process, the asset allocation is determined in the:A. planning step.B. feedback step.C. execution step9. The planning step of the portfolio management process is least likely to include an assessment of the client'sA. securities.B. constraints.C. risk tolerance.10. With respect to the portfolio management process, the rebalancing of a portfolio's composition is most likely to occur in the:A. planning step.B. feedback step.C. execution step.11. An analyst gathers the following information for the asset allocations of three portfolios:Which of the portfolios is most likely appropriate for a client who has a high degree of risk tolerance?A. Portfolio 1.B. Portfolio 2.C. Portfolio 3.12. Which of the following investment products is most likely to trade at their net asset value per share?A. Exchange traded funds.B. Open-end mutual funds.C. Closed-end mutual funds.13. Which of the following financial products is least likely to have a capital gain distribution?A. Exchange traded funds.B. Open-end mutual funds.C. Closed-end mutual funds.14. Which of the following forms of pooled investments is subject to the least amount of regulation?A. Hedge funds.B. Exchange traded funds.C. Closed-end mutual funds.15. Which of the following pooled investments is most likely characterized by a few large investments?A. Hedge funds.B. Buyout funds.C. Venture capital funds.Chapter 3 Portfolio Risk and Return: Part I PRACTICE PROBLEMS FOR CHAPTER 31. An investor purchased 100 shares of a stock for $34.50 per share at the beginning of the quarter. If the investor sold all of the shares for $30.50 per share after receiving a $51.55 dividend payment at the end of the quarter, the holding period return is closest to:A. - 13.0%.B. - 11.6%.C. - 10.1%.2. An analyst obtains the following annual rates of return for a mutual fund:The fund's holding period return over the three-year period is closest to:A. 0.18%.B. 0.55%.C. 0.67%.3. An analyst observes the following annual rates of return for a hedge fund:The hedge fund's annual geometric mean return is closest to:A. 0.52%.B. 1.02%.C. 2.67%.4. Which of the following return calculating methods is best for evaluating the annualized returns of a buy-and-hold strategy of an investor who has made annual deposits to an account for each of the last five years?A. Geometric mean return.B. Arithmetic mean return.C. Money-weighted return.5. An investor evaluating the returns of three recently formed exchange-traded funds gathers the following information:The ETF with the highest annualized rate of return is:A. ETF 1.B. ETF 2.C. ETF 3.6. With respect to capital market theory, which of the following asset characteristics is least likely to impact the variance of an investor's equally weighted portfolio?A. Return on the asset.B. Standard deviation of the asset.C. Covariances of the asset with the other assets in the portfolio.7. A portfolio manager creates the following portfolio:If the correlation of returns between the two securities is 0.40, the expected standard deviation of the portfolio is closest to:A. 10.7%.B. 11.3%.C. 12.1%.8. A portfolio manager creates the following portfolio:If the covariance of returns between the two securities is - 0.0240, the expected standard deviation of the portfolio is closest to:A. 2.4%.B. 7.5%.C. 9.2%.The following information relates to Questions 9-10A portfolio manager creates the following portfolio:9. If the standard deviation of the portfolio is 14.40%, the correlation between the two securities is equal to:A. - 1.0.B. 0.0.C. 1.0.10. If the standard deviation of the portfolio is 14.40%, the covariance between the two securities is equal to:A. 0.0006.B. 0.0240.C. 1.0000.The following information relates to Questions 11-14An analyst observes the following historic geometric returns:11 . The real rate of return for equities is closest to:A. 5.4%.B. 5.8%.C. 5.9%.12. The real rate of return for corporate bonds is closest to:A. 4.3%.B. 4.4%.C. 4.5%.13. The risk premium for equities is closest to:A. 5.4%.B. 5.5%.C. 5.6%.14. The risk premium for corporate bonds is closest to:A. 3.5%.B. 3.9%.C. 4.0%.15. With respect to trading costs, liquidity is least likely to impact the:A. stock price.B. bid-ask spreads.C. brokerage commissions.16. Evidence of risk aversion is best illustrated by a risk-return relationship that is:A. negative.B. neutral.C. positive.17. With respect to risk-averse investors, a risk-free asset will generate a numerical utility that is:A. the same for all individuals.B. positive for risk-averse investors.C. equal to zero for risk seeking investors18. With respect to utility theory, the most risk-averse investor will have an indifference curve with the:A. most convexity.B. smallest intercept value.C. greatest slope coefficient.19. With respect to an investor's utility function expressed as:21=E(r)-2u A ,which of the following values for the measure for risk aversion has the least amount of risk aversion?A. - 4.B. 0.C. 4.The following information relates to Questions 20-23A financial planner has created the following data to illustrate the application of utility theory to portfolio selection:20. A risk-neutral investor is most likely to choose:A. Investment 1.B. Investment 2.C. Investment 3.ExpectedStandard Deviation (% )28153021. If an investor's utility function is expressed as U = E(r) ~A& and the measure for risk aversion has a value of- 2, the risk-seeking investor is most likely to choose:A. Investment 2.B. Investment 3.C. Investment 4.22. If an investor's utility function is expressed as U = E(r) - ~A& and the measure for risk aversion has a value of2, the risk-averse investor is most likely to choose:A. Investment 1.B. Investment 2.C. Investment 3.23. If an investor's utility function is expressed as U =E(r) - ~A& and the measure for risk aversion has a value of4, the risk-averse investor is most likely to choose:A. Investment 1.B. Investment 2.C. Investment 3.24. With respect to the mean-variance portfolio theory, the capital allocation line, CAL, is the combination of the risk-free asset and a portfolio of all:A. risky assets.B. equity securities.C. feasible investments.25. Two individual investors with different levels of risk aversion will have optimal portfolios that are:A. below the capital allocation line.B. on the capital allocation line.C. above the capital allocation line.The following information relates to Questions 26-28A portfolio manager creates the following portfolio:26. If the portfolio of the two securities has an expected return of15%, the proportion invested in Security 1 is:A. 25%.B. 50%.C. 75%.27. If the correlation of returns between the two securities is - 0.15, the expected standard deviation of an equal-weighted portfolio is closest to:A. 13.04%.B. 13.60%.C. 13.87%.28. If the two securities are uncorrelated, the expected standard deviation of an equal-weighted portfolio is closest to:A. 14.00%.B. 14.14%.C. 20.00%.29. As the number of assets in an equally-weighted portfolio increases, the contribution of each individual asset's variance to the volatility of the portfolio:A. increases.B. decreases.C. remains the same.30. With respect to an equally-weighted portfolio made up of a large number of assets, which of the following contributes the most to the volatility of the portfolio?A. Average variance of the individual assets.B. Standard deviation of the individual assets.C. Average covariance between all pairs of assets.31. The correlation between assets in a two-asset portfolio increases during a market decline. If there is no change in the proportion of each asset held in the portfolio or the expected standard deviation of the individual assets, the volatility of the portfolio is most likely to:A. increase.B. decrease.C. remain the same.The following information relates to Questions 32-34An analyst has made the following return projections for each of three possible outcomes with an equal likelihood of occurrence:32. Which pair of assets is perfectly negatively correlated?A. Asset 1 and Asset 2.B. Asset 1 and Asset 3.C. Asset 2 and Asset 3.33. If the analyst constructs two-asset portfolios that are equally-weighted, which pair of assets has the lowest expected standard deviation?A. Asset 1 and Asset 2.B. Asset 1 and Asset 3.C. Asset 2 and Asset 3.34. If the analyst constructs two-asset portfolios that are equally weighted, which pair of assets provides the least amount of risk reduction?A. Asset 1 and Asset 2.B. Asset 1 and Asset 3.C. Asset 2 and Asset 3.35. Which of the following statements is least accurate? The efficient frontier is the set of all attainable risky assets with the:A. highest expected return for a given level of risk.B. lowest amount of risk for a given level of return.C. highest expected return relative to the risk-free rate.36. The portfolio on the minimum-variance frontier with the lowest standarddeviation is:A. unattainable.B. the optimal risky portfolio.C. the global minimum-variance portfolio.37. The set of portfolios on the minimum-variance frontier that dominates all sets of portfolios below the global minimum-variance portfolio is the:A. capital allocation line.B. Markowitz efficient frontier.C. set of optimal risky portfolios.38. The dominant capital allocation line is the combination of the risk-free asset and the:A. optimal risky portfolio.B. levered portfolio of risky assets.C. global minimum-variance portfolio.39. Compared to the efficient frontier of risky assets, the dominant capital allocation line has higher rates of return for levels of risk greater than the optimal risky portfolio because of the investor's ability to:A. lend at the risk-free rate.B. borrow at the risk-free rate.C. purchase the risk-free asset.40. With respect to the mean-variance theory, the optimal portfolio is determined by each individual investor's:A. risk-free rate.B. borrowing rate.C. risk preference.Chapter 4 Portfolio Risk and Return: Part II PRACTICE PROBLEMS FOR CHAPTER 41. The line depicting the risk and return of portfolio combinations of a risk-free asset and any risky asset is the:A. security market line.B. capital allocation line.C. security characteristic line.2. The portfolio of a risk-free asset and a risky asset has a better risk-return tradeoff than investing in only one asset type because the correlation between the risk-free asset and the risky asset is equal to:A. - 1.0.B. 0.0.C. 1.0.3. With respect to capital market theory, an investor's optimal portfolio is the combination of a risk-free asset and a risky asset with the highest:A. expected return.B. indifference curve.C. capital allocation line slope.4. Highly risk-averse investors will most likely invest the majority of their wealth in:A. risky assets.B. risk-free assets.C. the optimal risky portfolio.。
金融工程第2章
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问题
一项新完成的交易对未平仓数量有什么样 的影响？ 一天的交易数量能否比未平仓数量更大？
期权、期货及其他衍生产品（第八版） Copyright © John C. Hull 2012
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交易指令类型
期权、期货及其他衍生产品（第八版） Copyright © John C. Hull 2012 14
结算中心和场外市场
场外市场交易的传统结算方法是双边结算。 自2007~2009年金融危机以后，世界各国纷纷要 求标准化的场外衍生品交易通过中心结算机制来 进行结算。
期权、期货及其他衍生产品（第八版） Copyright © John C. Hull 2012
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期货交易例子 (P20-21)
某投资者于6月5日持有两份12月份到期的 黄金期货多头合约
合约规模为100盎司黄金 期货价格为1250美元 初始保证金为每份合约6000美元（总计 12000美元） 维持保证金为每份合约4500美元（总计 9000美元）
期权、期货及其他衍生产品（第八版） Copyright © John C. Hull 2012
期权、期货及其他衍生产品（第八版） Copyright © John C. Hull 2012
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表2-3 远期合约与期货合约的比较
远期合约 交易双方间的私下合约 非标准化 通常只有单一交割日 在合约到期时结算 通常会发生实物或现金交割
有信用风险
期货合约 交易所内的标准合约 标准化 有一系列的交割日 每日结算 合约通常在到期前会被平仓
变化量
2.76 2.44 2.19 2.00 1.86
金融工程重点总结
金融工程考试重点总结第一章：金融工程导论一、有效市场1、弱式有效市场：包括以往价格的所有信息.2、半强式有效市场:除了以往的价格信息之外，还包括公开披露的信息。
3、强式有效市场：除了以往信息和公开信息之外，还包括内部信息。
二、对金融工程的认识及其特点1、认识：金融工程是在20世纪80年代末和90年代初,在金融创新的基础上发展起来的一门新学科，它融合了金融学、经济学、投资学和工程学的相关理论,同时又吸收了数学、运筹学、物理学等学科的精髓部分，是一门以现代金融理论为支撑、以实务操作为导向、结合工程技术管理和信息加工处理的交叉性学科。
金融工程被正式确立为一门独立的学科，一般以1991年美国“国际金融工程师学会”（IAFE)的成立作为标志，表明了金融工程正式被国际社会所确认。
2、特点：实用化的特点：实践性、灵活性和可操作性综合化的特点：跨学科、交叉性和互补性最优化的特点：目的性、赢利性和抗风险性数量化的特点：严密性、准确性和可计算性创造性的特点：发散性、创新性和主观能动性三、金融工程与金融创新1、金融工程基本功能：套利(获得利润）＆套期保值（规避风险)2、金融创新方法:a、基本衍生工具的创新b、基本要素改变型的金融创新方法c、静态和动态复制型金融产品创新方法d、基本要素分解型的金融产品创新方法e、条款增加（组合）型金融产品创新方法f、技术发展型金融服务(产品）创新方法第二章：金融工程技术的应用一、金融衍生工具1、含义及特点：含义：衍生金融工具是给予交易对手的一方，在未来的某个时间点，对某种基础资产拥有一定债权和相应义务的合约。
特点：从基础金融工具派生出来的;金融衍生工具是对未来的交易。
金融衍生工具是现在对基础工具未来可能产生的结果进行交易。
交易结果在未来时刻才能确定盈亏。
二、套期保值1、基本原理:套期保值的基本原理是建立对冲组合，当产生风险的一些因素发生变化时，对冲组合的净价值保持不变。
一般来说，若保值工具与保值对象的价格正相关，我们就可利用相反的头寸(如多头对空头，或空头对多头）来建立对冲组合进行套期保值；若保值工具与保值对象的价格呈负相关，我们就可利用相同的头寸（如多头对多头，空头对空头）来建立对冲组合进行套期保值。
金融工程学第二章
对未来金融工程技术的展望
大数据与人工智能的融合应用
随着大数据和人工智能技术的不断发展，未来金融工程技术将更加注重数据驱动和智能化决策，提高金融服务的精准 度和个性化水平。
区块链技术的广泛应用
区块链技术具有去中心化、安全性高、可追溯等特点，将在金融工程领域发挥重要作用，如智能合约、数字货币等创 新应用。
05
案例分析与实践应用
案例分析：金融工程技术在风险管理中的应用
信用风险管理
通过金融工程技术，如信用评分 模型、信用违约互换等，对信用 风险进行量化评估和管理，降低
信贷风险。
市场风险管理
运用金融工程技术，如风险价值模 型、压力测试等，对市场风险进行 度量和监控，帮助投资者在波动市 场中保持理性决策。
金融工程学的背景
随着金融市场的发展和金融创新的不断涌现，传统金融学已无法 满足日益复杂的金融需求。金融工程学的出现填补了这一空白， 为金融市场的发展注入了新的活力。
第二章内容概述
01
02
03
04
金融工程工具
介绍金融工程中常用的工具和 技术，如期权、期货、掉期等 衍生产品，以及数值计算、蒙 特卡洛模拟等计算方法。
第二章内容总结
金融工程学的基本概念和原理
介绍了金融工程学的定义、发展历程、基本原理和核心思想，以及金融工程技术在金融市 场中的应用。
金融产品的设计与定价
详细阐述了金融产品的设计流程、定价方法和风险管理策略，包括股票、债券、期货、期 权等多种金融产品。
金融工程技术的实践应用
通过案例分析，探讨了金融工程技术在企业融资、投资决策、风险管理等方面的实践应用 ，以及面临的挑战和解决方案。
金融工具的种类与特点
金融工具的定义
金融工程应用教程-答案
金融工程习题解答第二章 远期合约1、如何区分远期价值和远期价格的不同含义。
答：远期合约的价值是合同的价值，用f 表示；远期价格F 是标的资产的理论价格，是远期合约价值f 为0时的交割价。
2、FRA 协议中的几个日期之间有何关系？答：FRA 协议中的几个日期之间的关系如下图所示：其中的确定日、结算日、到期日，遇到节假日及法定休息日向前延伸或向后顺延。
3、请解释远期合约用来套期保值和来投机的方法。
答：套期保值，是签订远期合约，将未来交易的利率或汇率固定下来，避免利率或汇率波动对于负债或收益带来的风险。
投机，是建立在某种预期的基础上，以承担风险为代价获取收益的远期交易。
当投资者预期标的资产将上涨时做多头，反之做空头。
4、解释为什么外币可以被视为支付已知红利率的资产？答：由于外币的隶属国对于存入银行的外币按一定的利率支付利息，故外币可看成支付红利的资产。
5、当一种不支付红利股票的价格为$40时，签订一份1年期的基于该股票的远期合约，无风险利率为10%(连续复利)，试问：(1) 远期价格为多少？远期合约的初始价值为多少？(2) 两个月后，股票的价格为$45，远期价格和远期合约价值各为多少？解：已知：S=40，T －t =1，r =10%。
交易日 起算日确定日 结算日 到期日(1) 根据公式(2-2-2)有：F=Se r (T-t )=40e 0.1×1=44.21(美元)，初始价值：f =0。
(2) 已知：S=45，T －t =10/12，r =10%。
根据公式(2-2-2)有：F=Se r (T-t )=45e 0.1×5/6=48.91(美元)根据公式(2-2-1)有：f =45－40=5(美元)。
7、已知美元的即期利率为5%，人民币的即期利率为2%。
当前的人民币对美元的汇率是6.80:1，我国人民币计息天数为365天，问：一年之后的人民币对美元的远期汇率是多少？解：已知：S =6.80，r =0.05，r f =0.02，由公式(2-4-1)有：8、远期利率协议某交易日是2010年5月12日星期三，双方同意成交1×4金额100万美元，利率为6.25%的远期利率协议，确定日市场利率为7%。
第二讲：金融工程的基本分析方法
为了找出该期权的价值， 可构建一个由
一单位看涨期权空头和 Δ单位的标的
股票多头组成的组合。为了使该组合在
期权到期时无风险， Δ必需满足下式
：
11 －0.5=9
=0.25
该无风险组合的现值应为：
2.25e 0.10.25 2.19元
由于该组合中有一单位看涨期权空头和 0.25单位股票多头，而目前股票市场为 10元，因此：
答案是一定的。
套利进程是： 第一步，买卖者按10%的利率借入一笔6个月资金〔假
定1000万元〕 第二步，签署一份协议〔远期利率协议〕，该协议规
则该买卖者可以按11%的价钱6个月后从市场借入资 金1051万元〔等于1000e0.10×0.5〕。 第三步，按12%的利率贷出一笔1年期的款项金额为 1000万元。 第四步，1年后收回1年期存款，得本息1127万元〔等 于1000e0.12×1〕，并用1110万元〔等于 1051e0.11×0.5〕归还1年期的债务后，买卖者净 赚17万元〔1127万元-1110万元〕。
无套利的价钱是什么？
无套利平衡的价钱必需使得套利 者处于这样一种境地：他经过套利构成 的财富的现金价值，与他没有停止套利 活动时构成的财富的现金价值完全相等 ，即套利不能影响他的期初和期末的现 金流量状况。
例子
假定如今6个月即期年利率为10% 〔延续复利，下同〕，1年期的即期利 率是12%。假设有人把今后6个月到1年 期的远期利率定为11%，试问这样的市 场行情能否发生套利活动？
风险中性定价法
在对衍生证券定价时，我们可以假定一切投资 者都是风险中性ቤተ መጻሕፍቲ ባይዱ，此时一切证券的预期收 益率都可以等于无风险利率r，一切现金流 量都可以经过无风险利率停止贴现求得现值 。这就是风险中性定价原理。
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1 ÙThe Time Value of Money!ÀJ K1.A bank must satisfy certain creditworthiness criteria in order to be able to accepta LIBOR quote from another bank and receive deposits from that bank at LIBOR.Typically it must have to have a£¤credit rating.A.AAAB.AAC.AaaD.Aa2.Derivatives traders regard£¤rates as a better indication of the”true”risk-free ratethan Treasury rates.A.LIBORB.NIBORC.HIBORD.SIBOR3.The most common type of repo is an£¤,in which the agreement is renegotiatedeach day.A.everyday repoB.overnight repoC.data repoD.term repo4.The n-year zero-coupon interest rate is sometimes also referred to as the n-year£¤,the n-year£¤,or just the n-year£¤.A.zero rateB.par rateC.spot rateD.zero5.The£¤for a certain bond maturity is the coupon rate that causes the bond priceto equal its par value£The par value is the same as the principal value¤.A.bond yieldB.spot rateC.par yieldD.forward rate6.A largefinancial institution can at no cost lock in the forward rate for a future timeperiod,so the value of 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prices in-crease.()9.When duration is used for bond portfolios,there is an implicit assumption that theyields of all bonds will change by the same amount.()10.The convexity of a bond portfolio tends to be greatest when the portfolio providespayments evenly over a long period of time.It is least when the payments are concentrated around one particular point in time.()11.By matching convexity as well as duration,a company can make itself immune torelatively large nonparallel shifts in the zero curve.However,it is still exposed to nonparallel/parallel shifts.()n!¶c)º1.LIBOR2.LIBID3.A Repo or Repurchase Agreement4.Repo Rate5.Zero Rates6.Bond Yield7.Forward Interest Rate8.Forward Rate Agreement(FRA)9.Duration10.The Duration of a Bond Portfolioo!O K1.A bank quotes you an interest rate of l4%Per annum with quarterly compound-ing©What is the equivalent rate with(a)continuous compounding and(b)annual compounding?41 ÙTHE TIME VALUE OF MONEY2.What rate of interest with continuous compounding is 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