4.Assume S = $40, r = 0 .08, Sigma = 0.3, Div. yield rate = 0. Consider a 91 day, $40-strike put. Draw the plots for each of the following calculations.

Actual price with 90-days to expiration when stock prices vary between $30 to $40 in $1 increments.

What is delta approximated price with 90 days to expiration?

What is the delta-gamma approximated price with 90 days to expiration?

What is the delta-gamma-theta approximated price with 90 days to expiration?