7. (Simple Pricing)

Use the code in the framework to price the following kinds of option:

a) Futures contract, price = 4200, volatility = 15%, strike = 3800, T = 0.5. The put option premium is fully margined (Haug, 2007 gives p = 65.6185).

b) European 6-month call option on an index with index level = 810, strike = 800, riskfree rate = 5%, volatility = 20% and dividend yield = 2% (Hull, 2006 gives c = 53.39 on a two-step binomial tree).

c) Nine-month American put option on a futures contract with futures price = 31, strike price = 30, risk-free rate = 5%, volatility = 30% (Hull, 2007 gives p = 2.84 on a three-step binomial tree).