Fin4014S Derivative Securities|Option Theory Assessment Answer

You will be assigned a date corresponding to options in a provided file containing real S&P 500 option data from Option Metrics. The file includes data about a put or call option traded on a specific  date with an expiry 30 days later of varying strikes. You should select the closest to ‘at the money’ call option on your date, the option with the strike price closest to the closing price of the S&P500 on that date.

Q1

a) Find the 3 month US treasury rate and the closing price of the S&P 500 for the day your option is traded. Using the implied volatility value from the option metrics file for your option as the volatility input to the Black-Scholes model (including a dividend yield), price your option in excel and compare to the mid-point of the option metrics bid/ask spread. Assume dividend yield is zero for this part.

b) Can you find a dividend yield using excel solver for which the B-S-M formula price matches the midpoint of the Option Metrics Bid/Ask spread exactly?

Q2

Use the data in question 1 and DATA|TABLE in excel (or any other software/programming technique) to produce graphs to show;

a) The sensitivity of the Black-Scholes option price to changes in σ.

Discuss your results  in relation to option theory.

b) The sensitivity of the Black-Scholes option price to changes in the time to maturity T. Discuss your results in relation to option theory.

c) The sensitivity of the Black-Scholes option price to changes in the interest rate r. Discuss your results in relation to option theory.

Q3

Using the option parameters from Q1, produce a graph comparing a call’s intrinsic value [defined as max(S-X,0)] and its Black-Scholes price. From the graph you should be able to deduce that it is never optimal to exercise early a call priced by the Black-Scholes formula. Discuss your results in relation to option theory.

Q4

Using an at the money put from your date in the options data file produce a graph comparing a put’s intrinsic value [defined as max(X-S,0)] and its Black-Scholes price. From the graph you should be able to deduce that it may be optimal to exercise early a put priced by the Black-Scholes formula. Discuss your results in relation to option theory.