Problem 36.5 A stock is currently trading for $40 per share. The stock will pay no dividends. The annual continuously compounded risk-free interest rate is 0.08, and the stock price volatility is 0.3. Consider a 40-strike put on 100 shares with 91 days to expiration. Using the delta-gamma approximation, estimate P($40.55). [answer:$177.10]

I have been following: Consider a nondividend paying stock. The annual continuously compounded risk-free interest rate is 0.08, and the stock price volatility is 0.3. Consider a 40-strike call on 100 shares with 91 days to expiration.

(a) Find the option Greek gamma.

call = = 0.0652.

(b) Estimate the value of C($40.75) using the delta-gamma approximation.

C_40 = $2.7804

= 0.5824.

C($40.75) = 2.7804 + 0.5824(0.75) + 0.5 0.75² 0.0652 = $3.2355.