**Question 904** option, Black-Scholes-Merton option pricing, option on future on stock index

A **six** month European-style **call** option on six month S&P500 index **futures** has a strike price of **2800** points.

The six month **futures** price on the S&P500 index is currently at **2740.805274** points. The futures underlie the call option.

The S&P500 stock index currently trades at **2700** points. The stock index underlies the futures. The stock index's standard deviation of continuously compounded returns is **25**% pa.

The risk-free interest rate is **5**% pa continuously compounded.

Use the Black-Scholes-Merton formula to calculate the option price. The call option price now is: