1. A common stock will have a price of either $85 or $35 in 2 months. A two month put option on the stock has a strike price of $40.
Create a riskless portfolio. Buy one put option. How many shares should you buy?
2. Consider an option on a dividend-paying stock when the stock price is $48, the strike price is $45, the risk-free interest rate is 6% per annum, the volatility is 30% per annum, and the time to maturity is two months. The dividend to be paid in 1 month is $2.
a. What is the price of the option if it is a European call?
b. What is the price of the option if it is an American call?
Use the Black Scholes formula to answer the questions above.
3. Consider a European call option on a non-dividend-paying stock where the stock price is $50, the strike price is $50, the risk-free rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months.
c. Calculate u, d, a and p for a two-step tree. [Use 4 decimal places in your calculations.]
d. Value the option using a two-step tree. [Give your final answer to 2 decimal places.]
4. Suppose that the premium on a European put option, p = $3. The time to maturity, T = 1 year. The strike price is $20. The stock price of the underlying common stock is $12 today. The risk-free interest rate is 8% per annum. The stock does not pay dividends.
Observe that there is an arbitrage opportunity.
Clearly state what the trader would do to make a profit.
5. Consider the following portfolio: You buy two July 2009 maturity call options on Dell with exercise price of 30. You also sell two July 2009 maturity put options on Dell with an exercise price of 40. The Call premium is $3.30 and the Put premium is $2.50.
Assume each option contract is for one share of stock.
e. What will be your profit/loss on this position if Dell is selling at $42 on the option maturity date?
f. What will be your profit/loss on this position if Dell is selling at $38 on the option maturity date?
g. At what stock price on the option maturity date will you just break even on your investment?
6. Consider an option on a non-dividend-paying stock when the stock price is $48, the strike price is $45, the risk-free interest rate is 6% per annum, the volatility is 20% per annum, and the time to maturity is five months. It can be shown that d1 = .7576 and d2 = .6285.
Create a delta neutral portfolio of call options and stock. Short 10,000 call options (100 contracts). How many shares would you buy or sell?