Garman-Kohlhagen Formula

$$V_t=e^{-y\tau}S_tN(d_1)-e^{-r\tau}KN(d_2),$$

where $N$ is the cumulative Normal Distribution and

$$d_1, d_2={\log\left({S_t\over K}\right)+(r-y\pm{\textstyle{1\over 2}}\sigma^2)\tau\over\sigma\sqrt{\tau}}.$$

If $y=0$, this is the standard form of the Black-Scholes formula.

See also Black-Scholes Theory

References

Garman, M. B. and Kohlhagen, S. W. ``Foreign Currency Option Values.'' J. International Money and Finance 2, 231-237, 1983.

Price, J. F. ``Optional Mathematics is Not Optional.'' Not. Amer. Math. Soc. 43, 964-971, 1996.