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Unformatted text preview: Final Review 1. BlackScholes 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 riskneutral probability of expiring ITM . Putcall parity implies P(S,K, T, r, ) D Ke rT N( d 2 ) SN( d 1 ). 2. RiskNeutral 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 riskneutral world, given the stock price at time t . And Q S T , the riskneutral 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 BlackScholes 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 dividendyield of then v D e T S. For options on currencies Use BlackScholes 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 Novymarx during the Winter '07 term at CHIC.
 Winter '07
 NovyMarx

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