91Ó°ÊÓ

Two-State Option Pricing Model The price of Tara, Inc., stock will be either \(\$ 50\) or \(\$ 70\) at the end of the year. Call options are available with one year to expiration. T-bills currently yield 5 percent. 1\. Suppose the current price of Tara stock is \(\$ 60\). What is the value of the call option if the exercise price is \(\$ 35\) per share? 2\. Suppose the exercise price is \(\$ 60\) in part (a). What is the value of the call option now?

Put-Call Parity A put option and a call option with an exercise price of \(\$ 85\) and three months to expiration sell for \(\$ 3.15\) and \(\$ 6.12\), respectively. If the risk-free rate is 4.8 percent per year, compounded continuously, what is the current stock price?

Time Value of Options You are given the following information concerning options on a particular stock: $$ \begin{aligned} \text { Stock price } & =\$ 74 \\ \text { Exercise price } & =\$ 80 \\ \text { Risk-free rate } & =6 \% \text { per year, compounded continuously } \\\ \text { Maturity } & =6 \text { months } \\ \text { Standard deviation } & =53 \% \text { per year } \end{aligned} $$ 1\. What is the intrinsic value of the call option? Of the put option? 2\. What is the time value of the call option? Of the put option? 3\. Does the call or the put have the larger time value component? Would you expect this to be true in general?

Use the Black-Scholes model for pricing a call, put-call parity, and the previous question to show that the Black-Scholes model for directly pricing a put can be written as follows: $$ P=E \times e^{-R t} \times N\left(-d_2\right)-S \times N\left(-d_1\right) $$