1. The information needed is:
Stock price = $39
Exercise price = $40
Time to maturity = 0.5 years
Risk-free rate = 10% per year
Stock volatility = standard deviation of 40%/year
Using the Black-Scholes option pricing formula, calculate the value of a European call option that will not pay a dividend. What is the intrinsic value of this option? What is the time value of this option?
2. Suppose that you have the following information about interest rates.
The price of a zero coupon risk-free bond maturing in one year is $994
The price of a zero coupon risk-free bond maturing in two years is $983
The price of a zero coupon risk-free bond maturing in three years is $970
First, calculate the yield to maturity for the three bonds. Second, calculate each of the one year forward rates. Third, draw a diagram that shows the term structure of interest rates for these bonds showing both YTM and forward interest rates.
3. Suppose you sell a call option with a strike price of $45 for $3 and sell a put option with a strike price of $45 for $2 on the same stock. What is the pattern of payoffs from this investment look like on a payoff diagram? What is the most that you can gain or lose from this investment strategy?