Suppose S = $ 37, r = 8 %, delta(the annualized dividend rate) is 3 %, sigma(the annualized standard deviation of the continously compounded stock returns) is 41 %. Suppose you own a $ 42 - strike call with 100 days to expiration and you wish to do the gamma neutral hadging by writing a specified number of $ 38 - strike calls which also have 100 days until expiration.


a) Using the Black-Scholes formula, compute the price of the $ 42 - strike call?



b) Using the Black-Scholes formula, compute the price of the $ 38 - strike call?



c) Compute the delta for the $ 42 - strike call?



d) Compute the delta for the $ 38 - strike call?



e) Compute the gamma for the $ 42 - strike call?



f) Compute the gamma for the $ 38 - strike call?



g) Compute the number of $ 38 - strike call that you need to write in order to make your resulting portfolio have zero gamma?



h) Compute the cash earned on the combined transaction?



i) Compute the delta for your resulting portfolio?



j) Compute cost of the stock less the cash earned in order to delta hedge your portfolio?