This article introduces European Exchange Options, developed by Margrabe in 1978, and offers a free a pricing spreadsheet.
They are a generalization of the Black-Scholes model and give the holder the right to exchange one asset for another. An exchange options can be considered a variant of a rainbow option with a zero strike.
Consider two assets with prices S1(t) and S2(t). A European-style option which gives the holder the to exchange asset 2 for asset 1 has a payoff of max(0,S1(T) – S2(T)), where T is the time to maturity
The option can exercised at maturity (European-style), or at any time at or before maturity (American-style). Margrabe (1978) asserted that European and American exchange options are equal in value. However, Bjerksund & Stensland (1993) proved that American exchange options are more valuable than their European counterparts.
Pricing Exchange Options in Excel
Exchange options require the volatility, price and dividend yield for both assets, together with their correlation coefficient.
Margrabe (1978) gives the following analytical equations for pricing exchange options.