An at-the-money forward call option is a call with a strike price equal to the forward price of the underlying stock. Mathematically, the strike price of this option is given by:
K = erT S
Where: K denotes the strike price; r is the risk-free rate; T is time to expiration; S is the current stock price.
For example, if the forward price of XYZ stock is $50, while its underlying price is currently at $48.88, the risk free rate is 9%, and the call option expires in 3 months, then the option is an ATM forward call because:
erT S = exp (9% × 3/12) × 48.88 = 50
That is, the forward price of the stock is equal to the option’s strike price.
