1. Assume S = $40, r = 0 .08, Sigma = 0.3, Div. yield rate = 0. Now, Consider a $40-strike put with 180 days to expiration. S = $40. What is delta-gamma-theta approximated price for the option after 1, 5, and 25 days. For each of these days, vary the price of the stock from $36.00 to $44.00 in $0.25 increments. Compare the actual premium with the predicted premium for each price point. At which price are the two equal?

2. 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?