A bank has written a call option on one stock and a put option on another stock. For the first option the stock price is 50, the strike price is 51, the volatility is 28% per annum, and the time to maturity is 9 months. For the second option the stock price is 20, the strike price is 19, and the volatility is 25% per annum, and the time to maturity is 1 year. Neither stock pays a dividend. The risk-free rate is 6% per annum, and the correlation between stock price returns is 0.4.

• 1)  Please derive an approximate linear relationship between the change in the portfolio value and the change in the underlying stocks, and then estimate the 10-day 99% VaR based on this relation.
  
• 2)  Using C/C++ or Java or Matlab to calculate the 10-day 99% Monte Carlo Simulation based VaR for the portfolio. Set the number of simulation to 5000.