期權定價與動態(tài)套利均衡分析-在線瀏覽
2024-12-05 16:16本頁面
【正文】 ange of the stock. 20 ? Is probability relevant to option pricing? S ? 60Su ? 90Sd ? 30qq?1Probability distribution Answer: 1. Directly: No! 2. Indirectly: Yes! q SProbability distribution is not relevant to No arbitrage pricing 21 — OneStep Binomial Model (Cont.) ? Notation )(111r a t er e s k l e s srrd o w nm o v e sp r i c et h ew h e nd e c r e a s elp r o pot i o n adupm o v e sp r i c et h ew h e ni n c r e a s elp r o pot i o n auf??????d r u? ?No Arbitrage S uSu ? S dSd ?? ?? ???uS r L c uS XdS r L c dS Xud? ? ? ?? ? ? ?m ax ,m ax ,00? ?? ?? ??????c cS u dLdc ucr u du du dReplicating : Short sale of riskless security 0?22 RiskNeutrality — RiskAversion ? A Mini Case — Tossing a Coin 5$10$0Head Tail Fair Game Fair Game 4$Risk premium Risk discount Investment Gambling Investors: riskaverse Gamblers: riskprefer From real economy be charged by casino riskneutral 6$23 — RiskNeutral Pricing ? ?? ?? ?c S Lc cu ddc ucr u d rr du dcru ru dcr pc p cu d u du du d? ? ??????????????? ?????????? ? ???1 111riskneutral probability mean or expectation on riskneutral probability discounted by riskfree rate Analysis bees very simple! p r du d? ?? ? ?1 ? ? ??p u ru dand In an imaginary world A riskneutral world 24 — What Kind of Problems Can Be Resolved in an Imaginary RiskNeutral World? ? Proposition : If a problem with its resolving procedure is fully irrelevant to people’s riskpreference, then it can be resolved in an imaginary riskneutral world and the solution would be still valid in the real world. ? Proposition : NoArbitrage equilibrium in financial markets is fully irrelevant to people’s riskpreference. Therefore, riskneutral pricing is valid equilibrium pricing. Riskneutral pricing and noarbitrage pricing must be equivalent to each other. 25 — RiskNeutral Pricing (MultiStep Binomial Model ) SuSdSSu2udSSd2??cucdc? ?0,m a x 2 XSuc uu ??? ?0,m a x Xu d Sc ud ??? ?0,m a x 2 XSdc dd ?? t=0 t=1 t=2 The Underlying Stock The Call 26 — RiskNeutral Pricing (Cont. ) ? ?? ?? ?? ?c r pc p cc r pc p cu uu udd ud dd?? ? ??? ? ???1111? ? ? ?? ?c r p c p p c p cuu ud dd? ? ? ? ?? 2 2 22 1 1? ?? ? ? ?? ?? ? ? ?? ?0,m a x1!!!1!!!00XSduppjnjnrcppjnjnrcjnjnjjnjnnjdujnjnjnj???????????????????????????????? ?Generalizing: 27 — A Mini Case The Underlying Stock The Call 10128
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