




版权说明:本文档由用户提供并上传,收益归属内容提供方,若内容存在侵权,请进行举报或认领
文档简介
1、CHAPTER FIVE: Options and Dynamic No-Arbitrage1 A Brief Introduction of OptionsAn option is the right of choice exercised in future. The holder (buyer, or longer) of the option has a right but not an obligation to buy or sell a special amount of the asset with a special quality at a pre-determined p
2、rice.Terms of Options Call and put Exercise price Expiration date American options (C and P) vs. European options ( c and p)2The payoff profiles of call and putCallPutLongShort+_XXSTST00LongShort+_XXSTST00In-the-money, out-of-the-money, at-the-money, intrinsic value and time value A Brief Introducti
3、on of Options (Cont.)3The Basic No-Arbitrage1) ,2) 3) ,4) If , then , 5) 4The Basic No-Arbitrage (Cont.)The underlying is a non-dividend-paying stockSuppose , then Arbitrage Immediate Cash Flow Position Cash Flow on the expired date Short a stockLong an European call Long riskless securityNet cash f
4、lowsArbitrage Opportunity!5The Basic No-Arbitrage (Cont.)PropositionIf the period to expiration is very long, the value of an European call is almost equal to its underlying.PropositionAn American call on a non-dividend-paying stock should never be exercised prior to the expiration date.6 The relati
5、onship between American options and European options?andConclusion:7The Parity of Call and Put The underlying is a non-dividend-paying stockS can be replicated by c, p and riskless securitySupposePosition Cash flow at Cash flow at time T time tBuy a shareShort a callLong a putShort treasuryNet cash
6、flowArbitrage!8 Relationship between exercise and forward price Non-dividend-paying stocks American call and put?9 Non-dividend-paying stocks American call and put (Cont.)Position Cash flow at Cash flow at time when put exercised time tShort a shareLong an Amer. callShort an Amer. putLong treasuryNe
7、t cash flow10 Non-dividend-paying stocks American call and put (Cont.) Underlying is dividend-paying stockPresent value of dividends at time tPresent value of a long stock forward positionPresent value of a short stock forward position11 Underlying is dividend-paying stockFor European call and putFo
8、r American call and putHolds for non-dividend-paying stock underlyingDividend paidProved!How to prove it?Please see the next page!12 Proof ofPosition Cash flow at Cash flow at time when put exercised time tShort a shareEffect of dividendsLong an Euro. callShort an Amer. putLong treasuryNet cash flow
9、13 Proposition!For an American call, when there are dividends with big amount, the call may be early exercised at a time immediately before the stock goes ex-dividend.Question:If there are n ex-dividend dates anticipated, whats the optimal strategy to early exercise an American call?Answer:Please re
10、ad the last paragraph of page 74 of the textbook.14Dynamic No-Arbitrage t=0 t=1 t=2Bond ABond B 15 Replication step by stepUsing Bond A and riskless security with market value to replicate Bond Bs value in the above step16 Replication step by step (Cont.)Replicating the blow binomial tree by using B
11、ond A and riskless security with market valueReplicating the left binomial tree by using Bond A and riskless security with market value17 Self-financingNotes:Dynamic replication is forward while the procedure of pricing is backwardShort sale is available for self-financing18Option PricingBinomial Tr
12、ees One-Step Binomial Model Non-dividend-paying stocks European callUsing the underlying stock and riskless security with market value to replicate the European call?Sensitivity of the replicating portfolio to the change of the stock.19 Is probability relevant to option pricing?Probability distribut
13、ionAnswer:Directly: No!Indirectly: Yes!Probability distribution is not relevant to No arbitrage pricing 20 One-Step Binomial Model (Cont.) NotationNo ArbitrageReplicating :Short sale of riskless security21Risk-Neutrality Risk-Aversion A Mini Case Tossing a CoinHeadTailFair GameFair GameRisk premiumR
14、isk discountInvestment Gambling Investors: risk-averseGamblers: risk-preferFrom real economy be charged by casino risk-neutral22 Risk-Neutral Pricingrisk-neutral probabilitymean or expectation on risk-neutral probabilitydiscounted by risk-free rateAnalysis becomes very simple!andIn an imaginary worl
15、dA risk-neutral world23 What Kind of Problems Can Be Resolved in an Imaginary Risk-Neutral World?Proposition : If a problem with its resolving procedure is fully irrelevant to peoples risk-preference, then it can be resolved in an imaginary risk-neutral world and the solution would be still valid in
16、 the real world.Proposition : No-Arbitrage equilibrium in financial markets is fully irrelevant to peoples risk-preference. Therefore, risk-neutral pricing is valid equilibrium pricing. Risk-neutral pricing and no-arbitrage pricing must be equivalent to each other.24 Risk-Neutral Pricing (Multi-Step
17、 Binomial Model ) t=0 t=1 t=2The Underlying StockThe Call25 Risk-Neutral Pricing (Cont. )Generalizing: 26 A Mini Case The Underlying StockThe Call t=0 t=1 t=2 t=0 t=1 t=2 Risk-Neutral Pricing:27 A Mini Case (Cont.) Dynamic No-Arbitrage Pricing:28 Implication of Risk-Neutral PricingMean or mathematic
18、al expectation with probability in the real worldDiscount rates with risk premiumRisk-free rate used as discount rates without risk premiumQuestion:Does risk-neutral probability exist and is it unique?Mean or mathematical expectation with risk-neutral probability in the imaginary world29Fundamental
19、Theorems of Financial EconomicsThe First Financial Economics Theorem:Risk-neutral probabilities exist if and only if there are no riskless arbitrage opportunities.The Second Financial Economics Theorem:The risk-neutral probabilities are unique if and only if the market is complete.The Third Financia
20、l Economics Theorem:Under certain conditions, the ability to revise the portfolio of available securities over time can dynamically make up for the missing securities and effectively complete the market.30 Problem and Inverse Problem many investors make portfolio changes each portfolios change is li
21、mited the aggregation creates a large volume of buying and selling to restore equilibrium implying arbitrage opportunity exists each arbitrageur wants to take as large position as possible a few arbitrageurs bring the price pressures to restore equilibriumInverse Problem:Knowing the market prices of
22、 securities, determine the markets risk-neutral probabilities.Problem:Knowing the markets risk-neutral probabilities, determine the market prices of securities.Unfortunately, are actual securities markets like this ? Are they incomplete ? So it would seem that we will not be able to solve the inverse problem; that is, although risk-neutral probabilities may ex
温馨提示
- 1. 本站所有资源如无特殊说明,都需要本地电脑安装OFFICE2007和PDF阅读器。图纸软件为CAD,CAXA,PROE,UG,SolidWorks等.压缩文件请下载最新的WinRAR软件解压。
- 2. 本站的文档不包含任何第三方提供的附件图纸等,如果需要附件,请联系上传者。文件的所有权益归上传用户所有。
- 3. 本站RAR压缩包中若带图纸,网页内容里面会有图纸预览,若没有图纸预览就没有图纸。
- 4. 未经权益所有人同意不得将文件中的内容挪作商业或盈利用途。
- 5. 人人文库网仅提供信息存储空间,仅对用户上传内容的表现方式做保护处理,对用户上传分享的文档内容本身不做任何修改或编辑,并不能对任何下载内容负责。
- 6. 下载文件中如有侵权或不适当内容,请与我们联系,我们立即纠正。
- 7. 本站不保证下载资源的准确性、安全性和完整性, 同时也不承担用户因使用这些下载资源对自己和他人造成任何形式的伤害或损失。
最新文档
- 医疗企业布袋管理办法
- 数智时代涉外商事纠纷解决之道
- 厨房配料使用管理办法
- 河南循环包装管理办法
- 1850年以来吴语文献的词汇演变与语法特征研究
- 民航包机乘客管理办法
- 高压变电站主接线系统优化设计研究
- 对话自我与外界:探索个体与社会的互动
- 培训机构抽成管理办法
- 办公利益制度管理办法
- 会议活动复盘报告
- 隧道安全运营管理制度
- 2025年银行从业资格考试公共基础知识必考题库及答案(共五套)
- 山东省2024年艺术类本科批美术与设计类第1次志愿投档情况表(公布)
- 2025-2030胶原酶产业发展分析及发展趋势与投资前景预测报告
- 血液净化中心护理工作总结
- 2025年当兵的心理测试题及答案
- 2025年中级管道工(四级)技能认定理论考试指导题库(含答案)
- 头端可弯曲负压吸引鞘在输尿管软镜碎石术处理长径≤2cm上尿路结石中的应用研究
- 重大活动交通保障应急预案
- 净水设备维保合同
评论
0/150
提交评论