21. Show that the at-the-money-forward call price (4) is approximately equal to (10)Remark...

21. Show that the at-the-money-forward call price (4) is approximately equal to

(10)

Remark: Expression (10) gives us a quick method for calculating the prices of ATMF calls. Two interesting points about expression (10):

(a) It depends on only three parameters (S_t, and T - t) and the constantn in particular, the cumulative normal distribution function N(.) is not involved.

(b) It shows that the price of at-the-money-forward calls are approximately linear in

These features make the formula above very easy to use in practice not only to obtain prices of ATMF options, but also to obtain quick estimates of implied volatility of such options. The next two questions illustrate these points.