The settlement price for the December call option on S&P 500 futures with an exercise price of 1675 is 60.70. This option is American style and expires on December 20. The number of days to expiration is 95. The option is written on the December S&P 500 futures contract; the current settlement price for this contract is 1669.25. Assume that the riskless interest rate is 0.40%. We will also need the cost of carry rate for the underlying asset. In this case, the asset is a futures contract. There is no storage cost associated with holding a futures contract, the owner does not receive any yield (e.g., no dividends or coupon payments), and in fact there isn't even an opportunity cost of funds because it costs nothing upfront to buy the contract. Therefore, the cost of carry rate for a futures contract is zero.
a. Assume that the volatility rate for S&P 500 futures is 10%. Using the ten-step binomial tree, what is the value of the December call option on S&P 500 futures with an exercise price of 1675?