Valuation and parities for exchange options

Valuation and parities for both European-style and American-style exchange options are presented in a general financial model allowing for jumps, the possibility of default, and “bubbles” in asset prices. The formulas are given via expectations of auxiliary probabilities using the change-of-numéraire technique. Extensive discussion is provided regarding the way that folklore results such as Merton's no-early-exercise theorem and traditional parities have to be altered in this more versatile framework.