American call and put options on futures on an index of stocks with a strike price of 23.2 dollars for both the options. The current index value is 25.2 dollars, the risk-free rate of interest is 7 percent per annum, continuously compounded, and the index’s volatility is 0.38 per annum. The index yields a dividend of $3 at 4.5 months (the ex-dividend date) from now. Use a five-step binomial model to calculate the current fair call and put option prices and find the following:
a) Current fair call option price.
b) Current fair put option price.