Consider a 6-month European put option with strike price of $2050 on a stock index if the current index value is $2000. The dividends paid by the stock included in the index can be approximated by a continuously compounded dividend yield of 4%. The risk-free interest rate is 6%. The standard deviation of the index price appreciation is =20%.

a) Find the value of this option using Cox-Ross-Rubenstein 2-step binomial option pricing model. Hand-write your entire solution (use of calculators are allowed)

b) Using Excel, find the value of this option using Cox-Ross-Rubenstein 10-step binomial option pricing model.

c) Using Excel or any other methods (except option price calculators), find the value of this option using Black-Scholes model