Section A: Short Answers (total 8 questions, 5 points each) Are the following statements correct? Give brief explanations 1. The price of an option written on a foreign exchange rate depends on whether the home currency is expected to appreciate or depreciate against the foreign currency. 2. Variance swap can be used to hedge the vega risk of an option portfolio. 3. Forward prices decrease with the volatility of the underlying asset. 4. Crank-Nicolson method is a combination of explicit and fully implicit finite difference methods, so it is conditionally stable. 5. Gamma neutral hedging strategy can be done by trading the risk-free asset and the underlying asset. 6. Vega for a Barrier option sometimes can be negative. 7. Antithetic variates are a way to improve the efficiency of the finite difference method by using the fact that Brownian motions are symmetric in distribution. 8. Asian options are path-dependent, and thus, they do not satisfy the Black-Scholes equation