Assume that you have .an equity index with spot price 500, dividend yield 3.00% and volatility 35% per atmum. The risk- free interest rates (annual compounding) are constant and equal to 4% The dividend yield and the volatility of the index are both constant for all maturities and the stock index evolves in. time following a Geometric Brownian motion (Black - Scholes model).

Find:

1. The price and the Greeks of a European Call option with strike K = 650 and maturity 1.5Y. Calculate the delta of the option.
2. Use Monte-Carlo simulation to calculate the prices and the sensitivities of an average-strike Asian Call option and an average-strike Asian Put option, both with maturity 5Y. The payol o an average-strike Asian Call option is equal to Payoif = max(S{5)-S_average, 0), where S_average is the arithmetic average of five annual observations of the index at S(1), S(2), S(3), S(4), S(5). Similarly, the payoff of art average-strike Asian Put option is equal to Payoff = max(S_average-S(5), 0). Calculate the delta of the put,
3. For the same underlying asset, use a five-step binomial tree tn price a chooser option, whose holder can every year, from year one until maturity (year five) can choose whether the option is d call or a put. The exercise price in every choice is K = 525. Calculate the delta of the option.