Pricing Commodity Derivatives Using Principal Component Analysis

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Commodity derivatives are financial instruments whose value is based on an underlying commodity. These derivatives can be used for hedging purposes or for speculation. The most common types of commodity derivatives are futures, options, and swaps.

Due to their seasonal nature, valuing commodity derivatives requires pricing models that are different from other financial instruments. Specifically, the commodity pricing models should be able to take into account seasonality and other deterministic factors.

The popular commodity pricing models are 2- and 3-factor models [1]. Reference [2] proposed a new, multi-factor pricing method based on Principal Component Analysis (PCA),

The article presents a multi-factor model for pricing commodity derivatives. A primary application is to price commodity swaptions. Swaptions are a relatively illiquid product in commodities market, and the natural flow tends to be one-sided.

Earlier, we have categorized the model calibration strategy into seasonal and non-seasonal. Intuitively, the futures contracts for a seasonal asset (such as power or gas) are less fungible than futures contracts for a non-seasonal asset (such as oil). Hence, we use a boot-strapping strategy to calibrate local volatilities for non-seasonal assets, but for seasonal assets we calibrate the local volatilities of each contract separately.

The current form of the multi-factor model is presented in a way that the volatility ratio and mean reversions do not have a term structure. But the model is easily extendable to include a t dependency of volatility ration and mean reversions. This “term structure” model will make it easier to fit market prices of swaptions across different tenors.

Briefly, a PCA-based multi-factor model was successfully developed to price commodity swaptions.

We believe that this approach has its merits. Our reservation is that PCA is an implicit factor model, and it’s difficult to associate the principal components with real-world risk factors.

What do you think? Let us know in the forum or comments below.

References

[1] Helyette Geman , Commodities and Commodity Derivatives: Modelling and Pricing for Agriculturals, Metals and Energy, 2005, Wiley 1st edition.

[2] Tim Xiao, Pricing Commodity Derivatives Based on A Factor Model, 2022, https://philarchive.org/rec/XIAPCD

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