Economics of derivative

Problem Set 5

Please show all work. Please use four decimal places for all calculations.

1. Given the following information, what is the price of a 3-month European put option on a non-dividend paying stock with a strike price of $30? Assume the risk free rate is 3% per annum with continuous compounding, the current price of a stock is $29 and the current price of a 3-month call on the stock with a strike price of $30 is $1.5.

2. What opportunities are there for arbitrage given the following information? A six- month European call option on a non dividend paying stock has a price of $2.25. The current stock price is $25 and the strike price is at $20. The risk-free rate is 2% per year with continuous compounding. How much profit would the arbitrageur earn?

3. Given the following data, show the profit from a strategy involving a straddle for the put, call and combined position. The price of a European call and put option are $5 and $6 respectively. Both of the options have a strike price of $30. Explain why a trader might be willing to enter into a straddle.

4. Use the following information to create a butterfly spread. Construct a table showing the payoff and profit from such a strategy at various prices (e.g., $40, $41, $42… $60). Four month call options are available with strike prices of $45, $50, and $55. The option prices are $5, $2, and $0.5 respectively.

5. Consider a two-step tree where the time step is 2 months. Let u and d equal 1.1 and 0.9 respectively. Find the value of a European call where the current stock price is $40 and the strike is $40. Assume the risk-free rate is 2% per annum with continuous compounding.

6. Consider a two-step tree where the time step is 3 months. Find the value of an American put with a strike price of $65 given that the current price of the stock is equal to $60. Assume that u and d equal 1.3 and .7 respectively and that the risk free rate is equal to 3% per annum with continuous compounding.

7. Find the values of delta for each step in the tree for problem 6. Comment on your answer.

Additional Problems to Consider

How can aggressive bull and bear spreads be created with calls and puts?

Why is an American put option more likely to be exercised the deeper in the money it goes holding all else constant? Why does a decrease in volatility make the early exercise of an American put more likely holding all else constant?

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