Consider pricing a call option with a strike price of $2400 with 4-month maturity on the S&P 500 index. For the purposes of this problem assume the S&P 500 can move up by 35% or down by 20% each two-month period, and that it is currently trading for $2400. The risk-free rate over each two month period is 0.5%. Use a two-period binomial tree as a framework.
(a) What would you estimate the value of the call option to be as of date 0?
(b) What would you estimate the value of the call option to be at date 1 if the S&P 500 went up in value? What if it went down?
(c) If you sold the option, how would you hedge your position by trading in the underlying asset? Be as precise as you can, i.e. outline what positions you would choose to hold from today to maturity.