# Who trades exchange options in practice (Margrabe's formula)?

I'm currently studying the pricing of the exchange option.

https://en.wikipedia.org/wiki/Margrabe%27s_formula

While I can appreciate the theory, who actually buys these options in practice? Are they standardised and traded on any exchanges (I would guess not)

Who sells these options? My obvious guess is investment banks would tailor this contract for a client if they client wanted a large exposure that somehow reflected the exchange option spread payoff.

But why would someone want to pay a lot of money (presumably the impllied vol would be high) to own this option, when maybe it could be approximated by owning vanilla puts and calls in various combinations instead.

TL;DR nice theoretical formula, but are these options ever traded in practice in any material way, or are they just the tools of academics in ivory towers?

NB: this option is difficult to search for in google ("exchange option" obviously extremely broad, spread option/Margrabe gives so many hits on academic pricing references)

• The framework / concept has utility when tackling other (real) pricing problems but no one has ever rung the desk asking for a Margrabe option... Dec 21 '18 at 6:11
• These do trade in commodities. Options on either calendar spreads, or "the arb" (Brent vs wti) are both traded.
– will
Feb 16 '19 at 9:18
• Actually many bonds have a "cheapest to deliver" feature which can also be valued using principals from this too.
– will
Feb 16 '19 at 9:21

Yes, you can say they are traded on listed options, but only for a few limited markets, and not that liquid relative to options on a single asset.

For instance, the commodity futures space, there are options on commodity spreads listed, and a strike of 0 would be the same as an exchange option.

These options have some liquidity in energy and grain markets, but not everywhere. In the energy space, options on both related markets like WTI-Brent, and on calendar spreads have had listed spread options. In the grain markets, like Corn or Soybean, it’s usually only the calendar spreads (exchanging one maturity with another) that are traded.

Typically only 2-3 strikes would be liquid in these exchange listed spread options, of which the strike of 0 , which would be the exchange option, is usually one of them.

See these links as an example:

crude WTI-Brent options

Another application in commodity trading is power transmission capacity. A power transmission line will be used to transport electricity from zone A to zone B if the price $$p_A$$ in zone A is smaller than the price $$p_B$$ in zone B, else it will remain idle. So the "payoff" of owning power transmission capacity $$A\rightarrow B$$ is $$(p_B-p_A)^+$$. This is a zero strike call option on the $$p_B - p_A$$ price differential and is therefore valued using Margrabe. If you can e.g. choose daily whether or not to transmit power, it would be valued as a strip of Margrabe options

As an example of an instrument priced using Margrabe, Mexico government sold exchange warrants a few times in the past. The program's goal was to reduce hard-currency debt and replace it by local currency debt. An investor would pay some premium for the warrrants and have the right later to tender some face amount of hard-currency (and external-law) government bonds and to receive in exchange some face amount of local-currency government bonds. An investor could use Margrabe to compute a model price and compare it with the price of the warrants in the market.

As an added complication, the warrant holder could choose which of several choices of hard currency bonds to tender (i.e. cheapest to deliver), and likewise which of several choices of local bonds to receive.

These warrants were cash instruments that traded like bonds. Not on exchange, not Trace-eligible (because foreign government), not derivatives.

• the extra complication makes it more complicated though. margrabe is strictly on two underlyings, whereas this is a multi-underlying option
– ZRH
Feb 16 '19 at 6:33
• I found this paper from 2005 hacienda.gob.mx/biblioteca_relacion_inv_ingles/… deciribing the outcome of one of the warrants (declaring it a success) and explaining how the warrants work. Mexico issued such warrants a few more times. Also I recall Philippines also issued similar exchange warrants. Feb 18 '19 at 21:42