8 Option Markets Problems. Answers are provided. Please use the formula sheet that is attached separately to answer questions. Please show all work.

Formulas: Options (Fin. 338) 1. Black-Scholes Option Pricing Model. Ct = S [N(d1)] - Xe-rT [N(d2)] Pt = Xe-rT [N(-d2)] - S [N(-d1)] Where: ln(S / X ) (r 0.5 2 )T d1 T d 2 d1 T And: N(-d1) = 1 - N(d1) N(-d2) = 1 - N(d2) And where: Ct = value of call option Pt = value of put option d1 = cumulative density function of d1 d2 = cumulative density function of d2 ln (S/X) = natural logarithm of (S/X) = annual standard deviation of underlying stock's rate of return (i.e., a measure of the underlying stock's price volatility) S = current market price of underlying stock X = exercise price of call option r = current annualized market interest rate (risk-free rate) [assuming the riskfree rate is continuously compounded] T = time remaining before expiration (in fraction [percentage] of a year) (Where T = [number of days remaining till expiration] / 360) Formulas: Options (Fin. 338) 1 2. Black-Scholes-Merton Option Pricing Model (with dividends): Ct = Se-yT [N(d1)] - Xe-rT [N(d2)] Pt = Xe-rT [N(-d2)] - Se-yT [N(-d1)] Where: y = stock dividend yield ln(S / X ) (r y 0.5 2 )T d1 T d 2 d1 T And: N(-d1) = 1 - N(d1) N(-d2) = 1 - N(d2) 3. Call Option Intrinsic Value (Ci): Ci = max [0, S - X] 4. Put Option Intrinsic Value (Pi): Pi = max [0, X - S] 5. Call Option Profit. Per Share Profit = max [0, V - X] - Call Premium 6. Put Option Profit. Per Share Profit = max [0, X - V] - Put Premium 7. Put/Call Parity Formula(s). pt = ct - St + X e -r T Where: ct - pt = St - X e -r T St = ct - pt + X e -r T Xe -r T = St + pt - ct 8. Put/Call Parity (with dividends) Formula: pt = ct - Ste-y T + Xe -r T Formulas: Options (Fin. 338) 2 Homework Problems: Options Markets (Fin. 338) 1. The stock of the McCall Corporation is currently trading at $42 per share. The stock's volatility as measured by its standard deviation is 20%. If the strike (exercise) price for a certain set of options on McCall stock carry a strike price of $40, and the options run for 6 months (180 days), determine the Black-Scholes model values for: N (d1), N (d2), N (- d1), and N (- d2). (Assume the risk-free rate is 10% and that the stock pays no dividends.) 2. Given the information in question one (1) above and your calculated values for N (d1), N (d2), N (- d1), and N (- d2), determine: a. The price (premium) one must pay for a call option (Ct) on McCall stock using the Black-Scholes model. b. How much of the call's value is composed of intrinsic value? How much of the call's value is composed of a time premium? (Explain how you determined these values.) 3. Given the information in question one (1) above and your calculated values for N (d1), N (d2), N (- d1), and N (- d2), determine: a. The price (premium) of a put option (Pt) for McCall stock using the BlackScholes model. (Use the put/call parity model to confirm your answer.) b. How much of the put's value (price) is composed of intrinsic value? How much of the put's value is composed of a time premium? (Explain how you determined these values.) 4. You are considering buying options on the stock of the Wallace & Fischer Corporation, a producer of jet aircraft engine parts. The company's stock is currently trading at $40 per share and historically has had a volatility measure (standard deviation) of 30%. The options you are considering buying have a strike (exercise) price of $44 and run for 6 months (180 days). If the risk-free rate currently stands at 9%, and the underlying stock for the Wallace & Fischer Corporation is offering a dividend yield of 1.25%, determine the Black-Scholes-Merton model values for: N (d1), N (d2), N (- d1), and N (- d2). 5. Given the information in question four (4) above and your calculated values for N (d1), N (d2), N (- d1), and N (- d2), determine: a. The price (premium) of a call option (Ct) for Wallace & Fischer stock using the Black-Scholes-Merton model. b. How much of the call's value is composed of intrinsic value? How much of the call's value is composed of a time premium? (Explain how you determined these values.) Homework Problems: Options (Fin. 338) 1 6. Given the information in question four (4) above and your calculated values for N (d1), N (d2), N (- d1), and N (- d2), determine: a. The price (premium) of a put option (Pt) on Wallace & Fischer stock using the Black-Scholes-Merton model. (Use the put/call parity model to confirm your answer.) b. How much of the put's value (price) is composed of intrinsic value? How much of the put's value is composed of a time premium? (Explain how you determined these values.) 7. A four month (120 day) call option on a certain stock has an exercise (strike) price of $62 and is currently selling for $10. If the corresponding put option for this same stock (with the same $62 strike price and four month expiration length) is selling for $15.40, what is the underlying stock's current market price? Use the put/call parity model to determine your answer. (Assume the current risk-free rate is 4%, and that the stock pays no dividends.) 8. Assume a 3 month (90 day) call option on Coreman & Steel Corporation (a maker of oil drilling equipment) stock is selling for $1.20. The corresponding put option (with the same strike price and three month expiration length) is selling for $6.70. If Coreman & Steel stock is currently trading at $19.70 per share, and has an annual dividend yield of 2.2%, at what strike price can the stock's three month put and call options can be exercised? (Assume a risk-free rate of 6.5%.) Homework Problems: Options (Fin. 338) 2 Answers to Homework Problems: Options Markets (Fin. 338) 1. N (d1) = 0.7792 (where d1 = 0.7694) N (d2) = 0.7350 (where d2 = 0.6280) N (- d1) = 0.2208 N (- d2) = 0.2650 2. a. $4.76 (call price) b. 3. a. $0.81 (put price) b. 4. N (d1) = 0.4362 (where d1 = - 0.1605) N (d2) = 0.3547 (where d2 = - 0.3726) N (- d1) = 0.5638 N (- d2) = 0.6453 5. a. $2.42 (call price) b. 6. a. $4.73 (put price) b. 7. $55.78 8. $25.50 Homework Problems: Options (Fin. 338) 3