Consider a European call option on a non-dividend-paying stock; when the option is written, the stock price is *S _{0}*, the volatility of the stock price is s, the strike price is

*K*, the continuously compounded risk-free rate is

*r*, and the term to expiration is

*T*; let

*c*be the price of the option. The Black-Scholes formula for the option price is

C. *c=**S**0**N(**d**1**)**–**K**e**–**rT**N(**d**2**)*

where *N(x)* is the cumulative probability distribution function for a standardized normal distribution and *d _{1}* and

*d*are parameters dependant on the structure of the option, the level of interest rates, and the volatility of the stock price.

_{2}13. (a) Using the terminology of the last question (re-printed above – Question 8 from the multiple choice section), specify the Black-Scholes formula for the price of a European put option on a non-dividend-paying stock

Formula for value of put option is

P = -S0N (-d1) + ke^(-rt)N (-d2)

(b) Explicitly describe the relationship of the parameters *d _{1}* and

*d*to the structure of the option, the level of interest rates and the volatility of the stock price and the relationship of the parameters to each other; use the notation of the last question (e.g., write the formulas for

_{2}*d*and

_{1}*d*)

_{2}(c) We found that for a dividend yielding stock that there was a simple enhancement possible to convert the result in question 3) to the case of a European call option on a dividend yielding stock. Let *q* represent the dividend yield and describe the enhancement (which we found appropriate in many representations). Also, show the result for the European call option on a dividend yielding stock (include the formula for *d _{1}* and

*d*).

_{2}