(a)
In next two questions , suppose Amazon stock is currently selling at $200 per share; and the 1-year risk-free rate is 0%. An at-the-money 1-year put on Amazon is selling at $30.
1. What is the no-arbitrage price of an at-the-money 1-year call option on Amazon?
2. Assuming Amazon stock’s volatility is constant at the level expected by investors, how many shares of stock would you need to buy to replicate the 1-year call?
(b)
For the following three questions consider three 3-month American call options with strike prices of $75, $80, and $85 and market prices of $8.99, $6.37, and $4.37, respectively. The stock underlying these options is priced at $80 and pays no dividends. Suppose the risk-free rate is 0%.
1. Based on the options’ implied volatilities in the Black-Scholes model, investors seem to expect:
a. The stock price will be log-normally distributed in 3 months
b. There is a greater than lognormal probability of extremely good news
c. There is a greater than lognormal probability of extremely bad news
d. There is a greater than lognormal probability of extreme good and bad news
e. None of above
Explain your answer
2. If the stock’s market beta is 1.0, which of the three call options has the highest market beta?
3. If the stock’s alpha is 2% per year, what is the alpha of the call option with a strike price of $75?
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