Abstract
The main aim of the present paper is to give an explicit formula of the price of the currency put-option with knock-out. In the real market, the purpose of holding the option is to hedge the currency-risk of a foreign asset. To lessen the hedging cost, the option is knocked-out if the price of the asset goes up enough at the expiration date of the option. So the knock-out of the option is measured by the level of the price at the expiration date of the foreign asset. The formula is given in section 2 and in section 3 we compare it with the pricing formula of the plain option by Black and Scholes[1]. The model must be essentially a multi-factor one since the exchange rate and the asset price are not perfectly correlated in general. We use an extension of Black-Scholes economy in which the risk-free rate is constant and the asset price is modeled by a geometric Brownian motion. The model is given in section 1.
