Hi,
I understand that these options can be valued using the standard BS, or MC....I was wondering if there's any reference that explicitly shows how to value an exchange option using a binomial tree? While I already have a value and greeks using standard formulae....I'm interested in doing the same using a binomial tree to build more intuition. So far.....google search shows nothing. Would appreciate any feedback. Thanks!

In retrospect, there wasn’t really anything special about Margrabe’s option to exchange one asset for another. That is exactly what “regular” options are: the option to exchange a given amount of cash for a stock, or vice versa. That is also why puts and calls are the same. These things are often easiest to see in FX markets, where the inherent symmetry between currencies should hit you in the face. To answer your question, consider the process for the ratio of the two asset prices. That will follow a geometric Brownian motion, and you can build a standard biomial tree to model it (or, better yet, its log). The resulting option price will be in units of the numeraire asset, so you’ll have to rescale your answer by its initial price.

Noob question, why doing a binomial tree if there’s a straightforward closed-form modeł?

From a practical perspective, it would be one way (arguably the simplest) to address the value of early exercise opportunities. Separately, I find some pedagogical value in the binomial model, since it’s based on very simple math and is easy to code. But, as you know, l like closed form solutions…

This is all standard and easy stuff by this stage. I discuss robust (not ADI not Craig-Sneyd (they were born during the Cold Wah) PDE and numerics for a wide range of European and American options using different FDM schemes and  checked the output  against the results in Collector's book. We did extensive testing.
I discuss the methods in my 2022 PDE book. 

. Binomial is ad hoc and a bit depressing. 
. We need to flag the assumptions on the parameters of these _approoximate_ closed solutions. PDE works for _all_ parameter ranges. It's not rocket science.
. With early exercise, one can apply the Schwartz correction at each time step.
. "I have only been using FDM recipes heuristics" not my words. 

https://wilmott.com/mp-files/a-short-hi ... roach.pdf/

And for sensitivities, I think I used the Cauchy-Kowaleski theory as discussed here

https://www.datasim.nl/application/file ... hesis_.pdf

Actually, similar to Peter Carr's operator calculus (2001). Funnily, I attended his original talk on this in Broad Street..

viewtopic.php?t=103052

To add one more answer to kat’s question, unlike with the PDE/FDM stories, you can actually do the full fledged economics of option pricing (replication + no arbitrage) on the binomial lattice. From a probabilistic perspective, the symmetric binomial random walk is the obvious discretization of a standard Brownian motion, so not ad hoc in the slightest.

To add one more answer to kat’s question, unlike with the PDE/FDM stories, you can actually do the full fledged economics of option pricing (replication + no arbitrage) on the binomial lattice. From a probabilistic perspective, the symmetric binomial random walk is the obvious discretization of a standard Brownian motion, so not ad hoc in the slightest.

I qualify my remarks on the numerical robustness of binomial; it is a useful heuristic method without a-priori stability and error estimates. Just saying.

I totally agree that the binomial model is an inferior numerical solution scheme, but I don’t think that was the point of the questions asked.

From a practical perspective, it would be one way (arguably the simplest) to address the value of early exercise opportunities. Separately, I find some pedagogical value in the binomial model, since it’s based on very simple math and is easy to code. But, as you know, l like closed form solutions…

I really like the idea of modelling the ratio. That’s perhaps all one needs!

Picking the right numeraire can sometimes simplify these kind of problems (especially in fixed income settings).

I totally agree that the binomial model is an inferior numerical solution scheme, but I don’t think that was the point of the questions asked.

Really? How can you be so certain? So, what was the point?

shows how to value an exchange option using a binomial tree? While I already have a value and greeks using standard formulae....I'm interested in doing the same using a binomial tree to build more intuition

inferior is ambiguous..

For intuition on expectation <-> PDE, use Feyman-Kac.

Expectation doesn’t have much to do with the theory of option pricing. Nor do PDEs. They both fall into the category of how to solve (analytically and/or numerically) for the value of specific instruments (and their related Greeks) after the theoretical solution has been worked out.

Thanks for all the responses. I start with Binomial trees to build intuition, check for basic (at-least for me) like 1. positions and transactions at time 0 and time of expiration, 2. how the portfolio grows and its changing components, 3. check for identities like MtM on option plus MtM on hedge plus interest cost should be zero....etc. I usually stick to just a one period tree to build the intuition.
While searching, I did find a gem and it has a binomial tree treatment of exchange options. Rubinstein's archive on the internet archive https://web.archive.org/web/20070622150346/http://www.in-the-money.com/pages/author.htm
It's a treasure trove!