1.) A stock price is currently $100. For the next six months there is 15% probability that the stock will appreciate 10% with 5% annualized drift. The risk-free rate is 2% per year with continuous compounding. The dividend is 1%. Value the following option using binomial tress and 12-time steps.
a.) What is the value of a six-month European put option with a strike price of $102.
b.) What is the value of a six-month American put option with a strike price of $98.
c.) Estimate how high the minimum strike price must be for it to be optimal to exercise the option immediately.
2.) Now take the current price of the Exxon (XOM) May ATM monthly expiry option.
Calculate using Black Scholes.
a. The dollar value of shares you would need to sell if you sold $20,000 worth of puts.
b. The dollar value of your portfolio in one week if the stock went up 5%.
c. The % return to your portfolio in one week if the stock went up 5%.