Investor wishes to price a 3-month put option on the SPX index traded on CBOE. Suppose the SPX is currently at 1400, and the put is at the money (i.e. currently the price of the index is exactly the same as the exercise price of the option written on this index.) Take the volatility to be 15% and the risk-free rate to be 6%.
a. Use a 1-period binomial tree to price the option.
b. Now use 2-period binomial tree to price the same option.
c. Use Black Sholes formula to price this option