You have a portfolio of options on the same stock, with a delta 200 million and vega 400 million. (a) (5) If the stock price suddenly falls by one dollar while the volatility does not change, how much do you expect your portfolio value to change? (b) (5) If the stock price does not change but the volatility suddenly goes up by one percentage point (0.01, or 1%), how much do you expect your portfolio value to change? (c) (10) If you want to alter your 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 long or short in order to make your portfolio to delta and vega neutral?