The Valuation Of American Exchange Options Under
Margrabe provides a pricing formula for an exchange option where the distributions of both stock prices are log-normal with correlated components. Merton has provided a formula for the price of a European call option on a single stock where the stock price process contains a compound Poisson jump component, in addition to a continuous log-normally distributed component. We use Mertonâ€™s analysis to extend Margrabeâ€™s results to the case of exchange options where both stock price processes also contain compound Poisson jump components. We show that there is a change in the distribution of the jump components in the equivalent martingale measure when jumps are present in the numÂ´eraire process. In the case of the American version of such options, the price is shown to be the solution of a free boundary problem. We solve this problem using a modification of McKeanâ€™s incomplete Fourier transform method due to Jamshidian. The resulting integral equation for the early exercise boundary is solved numerically. We compare the numerical integration solution with a method of lines approach
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
When requesting a correction, please mention this item's handle: RePEc:sce:scecf5:483. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum)
If references are entirely missing, you can add them using this form.