You short 200 contracts of a call option on Stock XYZ. The contract multiplier is 100, i.e. each contract is on 100 shares of the stock. Strike price is $50. The XYZ stock price is $52 right now. Option has 0.05 years left until expiration. The risk-free interest rate is 4% per year, and volatility of stock returns is 25% per year.

1. Using Black Sholes option pricing model, calculate the delta of the call position and determine the number of shares of the underlying stock that you need to buy to hedge the option position initially.

2. Calculate the amount of debt you need in order to buy the number of shares identified in part a, assuming you buy those shares entirely with borrowed funds.

3. Suppose that the next trading day, price of the stock decreases to $51. Time to expiration is now 0.04 years. The other parameters are unchanged. Recalculate delta and determine the number of shares you need to buy (sell) to trade to maintain the hedge.

4. Calculate the value of your debt position after you made the adjustment in part c. Hint: Interest rate in this problem is 4% per year, so the old debt calculated in part b has now earned 1 day, or 1/252 years, worth of interest.