(Option leverage; straddle payoffs; replication; % margin) In the one-period binomial model, the current stock price of CAT (Caterpillar) is $90. Robert expects that in one year the stock price of CAT will be either $108 (up move) or $75 (down move). The exercise price of one-year European call (or put) option of CAT=$100 and risk-free rate r=2% per annum. Robert would like to construct a portfolio with the stock and cash to replicate the payoff of 1,000 units of straddle of CAT, where one unit of straddle is the combination of long one call option and long one put option with the same strike price.

(a) What are the gross payoffs ($) of 1,000 units of CAT straddle in the up and down move, respectively?

(b) How many shares of CAT does Robert need to buy/short now?

(c) How much money does Robert need borrow/save now?

(d) Calculate the percentage margin.

[Note: percentage margin=(equity)/(short position) or percentage margin=(equity)/(value of stock)]

(e) Calculate the current price of CAT straddle (per unit) in the one-period binomial setting.