You have a portfolio of options on the same stock. Your portfolio has value II(S,t). At time t the delta of your portfolio is an/aS = -$300 million and the vega of your portfolio is alo $500 million. (a) (5 points) If the stock price suddenly falls by one dollar, while the volatility does not change, how do you expect the value of II to change? (b) (5 points) If the stock price does not change, but the volatility suddenly goes up by one percentage point (0.01 or 1%), by how much do you expect your portfolio value to change? (C) (10 points) If you want to alter you risk exposure using (i) the underlying stock and (ii) a put option with a delta of -0.5 and a vega of 20, how many of these two contracts do you need to go long or short to make your portfolio delta and vega neutral (i.e. alo = 0 at time t = t)? You have a portfolio of options on the same stock. Your portfolio has value II(S,t). At time t the delta of your portfolio is an/aS = -$300 million and the vega of your portfolio is alo $500 million. (a) (5 points) If the stock price suddenly falls by one dollar, while the volatility does not change, how do you expect the value of II to change? (b) (5 points) If the stock price does not change, but the volatility suddenly goes up by one percentage point (0.01 or 1%), by how much do you expect your portfolio value to change? (C) (10 points) If you want to alter you risk exposure using (i) the underlying stock and (ii) a put option with a delta of -0.5 and a vega of 20, how many of these two contracts do you need to go long or short to make your portfolio delta and vega neutral (i.e. alo = 0 at time t = t)