Problem 1. A firm has just sold a call option for 100 shares of a stock, with a strike price of 55 dollars per share, and time to maturity is 9 months. The current price of the stock is 54 dollars. Assume the volatility of the stock is = 0.35 and the continuous compound interest rate is 10 percent. The firm uses delta hedging to reduce the risk that the stock price will go up. Consider four possible scenarios.

Case 1. After 1 month, the stock price remains unchanged at 54 dollars per share.

Case 2. After 1 month, the stock price goes up to 65 dollars per share.

Case 3. After 1 month, the stock price goes up to 60.05 dollars.

Case 4. After 1 month, the stock price goes up to 60 dollars and volatility rises to 0.45.

In each case, calculate the three relevant items on the Balance Sheet of the firm (i.e. Options, Stock, Debt), and the Total at the bottom of the balance sheet. Remark: In the example we did in class, the three items on the balance sheet are labelled as: Change in Value in 100 Short Calls, Long Position in the Stock, Interest Expense. The Total at the bottom is labelled as: Total Change in Value. To find the value of N(x) for any number x, use the function in Excel Spreadsheet, norm.dist(x,0,1,true).

Problem 2. For the problem above, consider Case 2. Suppose the firm did not do any hedging. Calculate what would have been the loss, resulting from the change in liabilities on the Balance Sheet of the firm. Note: This loss is due to the short position for the call option of 100 shares.

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