1. The goals of this assignment are (i) to understand how call and put option prices vary with the exercise price, the underlying stock price, and the time to maturity, (ii) to compute option prices using Black-Scholes model, and (iii) to understand put-call parity.
Do the following.
a) Compute the intrinsic value and time value for 4 optionsfor the second-month expiry contracts as of the close of the 9th week of class. That is, if we are in November, then choose the January-expiry contract. The 4 options are: (i) nearest in-the-money call, (ii) nearest out-of-the-money call, (iii) nearest in-the-money put, and (iv) nearest out-of-the-money put options.Thus if stock price is $582, then chose options with X = 580 and 590. Can the intrinsic value be negative? Can the time value be negative?
b) In addition to the 4 options mentioned above, collect the premiums for the next nearest moneyness options; that is, consider the call and put options on X = 570 and X = 600 options also. Thus, you'll have 4 call option and 4 put options.Plot the call and put premium as a function of the exercise price for both the call and put options. Confirm that the call premium decreases with exercise price and the put premium increases with exercise price.
c) Find the nearest in-the-money call option and the nearest out-of-the-money put option on the first day; that is, consider the call option and put option with X = 580. Collect the closing option price and closing stock price for 4 days for these 2 options. Sort the data based on stock price. Then plot the call and put premiums against the stock price for the 4 days. Confirm that the call premium increases with stock price and the put premium decreases with stock price.
d) Find the nearest in-the-money call option and the nearest out-of-the-money put option on the first day; that is, consider the call option and put option with X = 580. Collect the closing option price for 4different maturities (starting with nearest maturity) for these two options.Make sure that the nearest maturity is between 30 and 60 days from current date. Plot the call and put premiums against the days remaining to maturity. Confirm that the call and putpremium increases with time to expiration.
e) Compute the B-S value for in-the-money call option (X=580). Compute volatility based on daily returns computed over the prior two-month period (download daily GOOG prices and compute returns using adjusted closing prices for the 60 trading days prior from Yahoo.com).
To obtain the relevant risk-free rate for pricing these options, do the following after market close on the day of the class. Go to WSJ.com. Then click on "Markets", then "Market Data." Scroll down to the section on "Bonds, Rates and Credit Markets." Click on "See All Treasuries." Then under "Treasuries," click on "See Full Daily Closing Prices." Then click on "Bills." Then get the Treasury yield ("Asked yield") of the bill whose maturity is closest to the expiry date of the option contract you are interested in. Clearly specify the maturity of the Tbill that you use.
f) How does B-S call price compare with the actual call price?
g) Compute the B-S value (using the formula)for the out-of-the-money put (i.e., same exercise price as the in-the-money call). Also compute the put price using put-call parity, and confirm that both give you the same answer.
h) How does B-S put price compare with the actual put price?