Perpetual American Put Option Greeks

Assume that the stock price follows the process (2) dS(t) = rS(t)dt + oS(t)dW(t) where the risk-free rate is r. We assume zero dividend yield q = 0. i) Derive the Delta and Gamma of the perpetual American put options in the Black-Scholes model. Draw the plots of Delta and Gamma as functions of the spot stock price So for K = $100, r = 5%,0 = 25%. Assume that the stock price follows the process (2) dS(t) = rS(t)dt + oS(t)dW(t) where the risk-free rate is r. We assume zero dividend yield q = 0. i) Derive the Delta and Gamma of the perpetual American put options in the Black-Scholes model. Draw the plots of Delta and Gamma as functions of the spot stock price So for K = $100, r = 5%,0 = 25%