Problem 1

Consider a publicly traded company whose stock price is currently equal to $100 and whose volatility is 30% per year. Interest rates are 0%. You are holding the following portfolio:

100 shares of stock

50 call options with a strike of $110 expiring in 60 days (remember that there are 252 trading days in a year)

25 put options with a strike of $90 expiring in 62 days

1.Calculate the value of your portfolio.

2. Calculate the D, G, W and k of your portfolio.

3. If the price goes up by $2 suddenly, what is the value of your portfolio after that change?

Assume that the price of the stock is again $100. You want to delta-hedge your portfolio by buying shares of stock. Describe your hedging transaction. Make sure you do not change the value of your portfolio.

4. Assume that one day has passed and the stock price declined to $99. What is your hedged portfolio worth? Has your strategy worked?

5. Now assume that three more days have passed and the price of the stock is again at $100. You want to delta, and gamma hedge your portfolio by trading in shares of stock and in in put options with a strike of $100 and that expire in 100 days. Describe your hedging strategy.

6. After you implemented the hedge in part 5, you notice that the stock price changes from $100 to $101. How did the value of the hedged portfolio change? Will your portfolio continue to remain delta-hedge hedged? Comment on why, or why not.