FinalReview

FinalReview - Final Review 1. Black-Scholes C(S,K,T, r, ) D...

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Unformatted text preview: Final Review 1. Black-Scholes C(S,K,T, r, ) D SN(d 1 ) Ke rT N(d 2 ) where d 1 D ln S K C r C 2 2 T p T d 2 D d 1 p T . Interpretation: N(d 1 ) D # of shares in the replicating portfolio N(d 2 ) D risk-neutral probability of expiring ITM . Put-call parity implies P(S,K, T, r, ) D Ke rT N( d 2 ) SN( d 1 ). 2. Risk-Neutral Pricing The price of the European style call option is: C K (S t , T t) D e rT E Q t h max [0, Q S T K] S t i where E Q t [ j S t ] denotes the expected value in the risk-neutral world, given the stock price at time t . And Q S T , the risk-neutral price, is distributed lognormally ln Q S T S ! D N (r 2 2 )T, p T . Always useful to remember that if is normally distributed then E [e ] D e E[ ] C 1 2 Var[ ] . 3. Extension of Black-Scholes If the underlying pays a dividend, then C( v , K,T, r, ) D v N(d 1 ) Ke rT N(d 2 ) where d 1 D ln v K C r C 2 2 T p T d 2 D d 1 p T . and v is the appropriate underlying. If S pays a known dividend of D then v D S PV (D). If S pays a dividend-yield of then v D e T S. For options on currencies Use Black-Scholes for a stock that pays dividend...
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This note was uploaded on 08/14/2009 for the course BUS 35100 taught by Professor Novy-marx during the Winter '07 term at CHIC.

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FinalReview - Final Review 1. Black-Scholes C(S,K,T, r, ) D...

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