Consider a 40-strike call with 365 days to expiration. Graph the results from the following calculations.

a. Compute the actual price with 360 days to expiration at $1 intervals from $30 to $50.

b. Compute the estimated price with 360 days to expiration using a delta approximation.

c. Compute the estimated price with 360 days to expiration using a delta-gamma approximation.

d. Compute the estimated price with 360 days to expiration using a deltagamma theta approximation.