Consider a 40-strike call with 91 days to expiration. Graph the results from the following calculations.
a. Compute the actual price with 90 days to expiration at $1 intervals from $30 to $50.
b. Compute the estimated price with 90 days to expiration using a delta approximation.
c. Compute the estimated price with 90 days to expiration using a delta-gamma approximation.
d. Compute the estimated price with 90 days to expiration using a delta-gammatheta approximation.