(18 points) Suppose you hold a delta-hedged portfolio comprised of a stock and its derivatives. The portfolio's delta will drop by 3000 when the underlying stock price goes up by $1 and the portfolio value will drop by $60 when the stock's return volatility goes up by 100 basis points. There are two traded options A and B written on the same underlying stock as the portfolio. When the underlying stock price increases by $1, the value of options A and B will increase by $0.50 and $0.10, respectively, and the delta of options A and B will increase by 0.60 and 0.50, respectively. In addition, when the stock's return volatility goes up by 100 basis points, the value of options A and B will go up by $0.02 and $0.015, respectively. What is your hedging strategy if you want to make the portfolio delta-neutral, gamma-neutral and vega-neutral simultaneously? Suppose you decide to use the options A and B and the underlying stock as hedging instruments. You need to show clear derivation steps. (18 points) Suppose you hold a delta-hedged portfolio comprised of a stock and its derivatives. The portfolio's delta will drop by 3000 when the underlying stock price goes up by $1 and the portfolio value will drop by $60 when the stock's return volatility goes up by 100 basis points. There are two traded options A and B written on the same underlying stock as the portfolio. When the underlying stock price increases by $1, the value of options A and B will increase by $0.50 and $0.10, respectively, and the delta of options A and B will increase by 0.60 and 0.50, respectively. In addition, when the stock's return volatility goes up by 100 basis points, the value of options A and B will go up by $0.02 and $0.015, respectively. What is your hedging strategy if you want to make the portfolio delta-neutral, gamma-neutral and vega-neutral simultaneously? Suppose you decide to use the options A and B and the underlying stock as hedging instruments. You need to show clear derivation steps