The Black-Scholes formula for pricing a European call option at time t on a stock that...

 

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The Black-Scholes formula for pricing a European call option at time t on a stock that pays dividends at the continuous rate 5 is (1) where C(t, S., K,o,r,T. 5) Ser-06(d)- Ke(-)(d) di In(S./K)+(r-6+0)(1) OVT-1 d-d-oT-t In equation (1), S, is the current price of the stock, K is the strike price of the option, o is the volatility of the stock, r is the continuously compounded risk-free interest rate, T is the time to expiration, & is the dividend yield on the stock, and is the CDF of the standard normal distribution. Formula Greek Delta Symbol A (7 (ds) Gamma e-(T-1) '(4) S01- In the table above d'() = (-) where o is the PDF of the standard normal distribution. 1 6(x)= 2m -81118 Problem 1 (15 pt). Consider a Black-Scholes market. (a) What happens to the European call option price as K0? (b) What happens to the European call option price as a-07 (c) Use the Put-Call Parity formula to derive the Black-Scholes formula for a Euro- pean put option. [Hint: for any r, 1-(x) = (-1)] The Black-Scholes formula for pricing a European call option at time t on a stock that pays dividends at the continuous rate 5 is (1) where C(t, S., K,o,r,T. 5) Ser-06(d)- Ke(-)(d) di In(S./K)+(r-6+0)(1) OVT-1 d-d-oT-t In equation (1), S, is the current price of the stock, K is the strike price of the option, o is the volatility of the stock, r is the continuously compounded risk-free interest rate, T is the time to expiration, & is the dividend yield on the stock, and is the CDF of the standard normal distribution. Formula Greek Delta Symbol A (7 (ds) Gamma e-(T-1) '(4) S01- In the table above d'() = (-) where o is the PDF of the standard normal distribution. 1 6(x)= 2m -81118 Problem 1 (15 pt). Consider a Black-Scholes market. (a) What happens to the European call option price as K0? (b) What happens to the European call option price as a-07 (c) Use the Put-Call Parity formula to derive the Black-Scholes formula for a Euro- pean put option. [Hint: for any r, 1-(x) = (-1)]

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a As K0 the call option becomes deeply inthemoney Using LHopitals ... View the full answer