3. At the close of the trading day you sell an at-the-money 6-month European call on a non-dividend paying stock trading at $40.00 with an implied volatility of 50% when the continuously-compounded rate of interest is 8%. This is the only position in your account. Your risk-management department tells you that the 99% coverage price range is $6.0 and the 99% volatility coverage range is 20%. (a) Use your Black-Scholes option pricer to calculate (and fill in the table below) your profit/loss if you buy back your short option as a function the changes in stock price and volatility indicated (i.e. premium - cost of option with different stock price and volatility). Volatility Stock Price 0.40 0.45 0.50 0.55 0.60 32.5 34.0 35.5 37.0 38.5 1.96 40.0 0.00 41.5 43.0 44.5 46.0 47.5 (b) If the risk appetite of the the firm that guarantees the performance of your trades is that no account should lose money for 99% of movements of the primary risk dimensions (stock price and volatility in this case), referring to the table above how much cash would you need to have in your account to put this position on? (c) If you only have the premium you made on the sale in your margin account will you be on call? (d) Using the values in the table and the centered finite-difference formula discussed in lecture, calculate the delta of your position if the volatility decreases to 45%.