4. (European FX option.) Suppose you know that the current value of the peso
dollar exchange rate is 3.75 pesos per dollar. The yearly volatility of the Mexican peso is 20%.

The Mexican interest rate is 8%, whereas the US rate is 3%. You will price a dollar option written on the Mexican peso. The option is of European style and has a maturity of 270 days. All processes under consideration are known to be geometric.

a. Price this option using a standard Monte Carlo model. You will select the number of series, the size of the approximating time intervals, and other parameters of the Monte Carlo exercise.

b. Now assume that Mexico’s foreign currency reserves follow a geometric SDE with a volatility of 10% and a drift coefficient of 5% a year. The current value of reserves is USD7 billion. If reserves fall below USD6 billion, there will be a one-shot devaluation of 100%. Is this information important for pricing the option? Explain.

c. Use importance sampling to reprice the option. Your pricing is supposed to incorporate the risk of devaluation