3. At the close of the trading day you sell an at-the-money 11-month European put on a non-dividend paying stock trading at $36.50 with an implied volatility of 40% when the continuously-compounded rate of interest is 7%/year. 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). Stock Price 0.32 0.36 Volatility 0.40 0.44 0.48 29.0 30.5 32.0 33.5 35.0 36.5 -1.60 0.00 38.0 39.5 1.48 41.0 42.5 44.0 (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) Using the values in the table and the centered finite-difference formula discussed in lecture, calculate the delta of your position if the volatility suddenly decreased to 36% with all other variables remaining the same.