Commodity Option Pricing: A Practitioner's Guide

2.8 COMMODITY SWAPTIONS

Järvinen and Toivonen (2004) and Larsson (2011) introduce these products, which are not covered extensively in the literature by any means, but which are relevant particularly for the coal market.

An Asian option is an option on the arithmetic average which pays the positive component of the difference at expiry between the discretely monitored arithmetic average over the fixing times {t₁, …, t_n} and strike (subject to different sign convention for calls and puts). Note that the exercise decision is made at the point in time when the last fixing is determined, and generally settlement occurs five business days later.

In contrast, a swaption is an option on a forward swap which requires the holder to elect whether to exercise the swaption before the swap commences (unlike an Asian option, which is more like a European option referenced against an underlying swap). An Asian option is exercised (or not) once all the fixings have been determined, whereas the decision rule for a commodity swaption necessarily has to be with respect to an underlying forward swap.

Let t₀ = T denote the expiry date of the swaption, and t₁, …, t_n the fixing dates for the underlying commodity swap, with t₀ < t₁ < … < t_n. Typically, the swap will be marked against the prompt futures, so each cashflow will be of the form . We shall not concern ourselves here with swaptions referenced ...