An exchange option holder has the right to exchange one asset for another. The option can be either European (allowing the exchange only on the Maturity Date) or American (allowing the exhange on any date up to and including the Maturity Date).
For example, a fund manager might purchase an exchange option if he is sure that he wants to hold one of two stocks but is unsure of which. The option would then allow the fund manager to hold one stock and then switch it for the other depending on the relative performance of the two stocks during the option's life.
Exchange options require numerous inputs to the valuation model in addition to the Black Scholes inputs. Two volatilities, spot prices and yields must be input (one for each asset) The correlation between the assets must also be be estimated, the correlation is a measure of the dependency of the two assets, if asset A moves up or down in direct tandem with Asset B then the two assets will have a correlation of 1 (or 100%). The higher the correlation of the assets the lower the option value will be.