What is the price of the put according to the Black-Scholes equation? Under what circumstances does the investor make a profit? Under what circumstances will the option be exercised?

Homework AD 717

Week 11

Problem 1.
An investor buys a European style put option. The stock price is $42 and the strike price is $40. The option has ninety days until maturity. The risk–free rate stands at 1.6%, and the volatility of the stock returns is 49%.
a) What is the price of the put according to the Black–Scholes equation?
b) Under what circumstances does the investor make a profit?
c) Under what circumstances will the option be exercised?
d) Draw a diagram showing the variation of the investor’s profit with the stock price at the maturity of the option.
e) Sketch how the value of the option varies with the stock price three months out, one month out, and on maturity

Problem 2.
Traders can use multiple strategies when they are bullish on the stock of a company. Two examples are
(i) writing a put option and (ii) buying a call option. Let us assume the stock does not pay a dividend.
a) Draw the payoff diagram at maturity for the put option and the call option. The put option has a strike price of $40, and it trades for $2. The call option has a strike price of $45, and it trades for $1.
b) List the maximum possible gains and losses for each strategy.
c) If the option is European style, it can only be exercised at maturity. American style options can be exercised at any time. Explain how this affects the strategies of the option seller and of the option buyer.