Theoretical value of a callThis model, developed to evaluate currency options, considers foreign currencies analogous to a stock providing a known dividend yield. The owner of foreign currency receives a “dividend yield” equal to the risk-free interest rate available in that foreign currency. The model assumes price follows the same stochastic process presumed in the Black-Scholes model.
This model is used to evaluate options written on currencies. The interest rate of the native currency is used as the default, but you can set the foreign interest rate in Model preferences.
This model corrects the difference between native and foreign interest rates. However, as a modification of Black-Scholes model, it possesses all its limitations.
Notation
Theoretical value of a call
Theoretical value of a put
Underlying price
Strike price
Interest rate
Interest rate in the foreign country
Time to expiration in years
Volatility
The European call price is given by:
Where:
The European put price is given by:
