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A multi-factor jump-diffusion model for commodities

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Crosby, John

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Abstract In this paper, we develop an arbitrage-free model for the pricing of commodity derivatives. The model generates futures (or forward) commodity prices consistent with any initial term structure. The model is consistent with mean reversion in commodity prices and also generates stochastic convenience yields. Our model is a multi-factor jump-diffusion model, one specification of which allows the prices of long-dated futures contracts to jump by smaller magnitudes than short-dated futures contracts, which, to our knowledge, is a feature that has not previously appeared in the literature, in spite of it being in line with stylised empirical observations (especially for energy-related commodities). Our model also allows for stochastic interest-rates. The model produces semi-analytic solutions for standard European options, which enable option prices to be evaluated in typically about 1/50th of a second (depending upon parameter values and the required accuracy). This opens the possibility to calibrate the model parameters by deriving implied parameters from the market prices of options. We perform such a calibration on crude oil options and show that, allowing long-dated futures contracts to jump by smaller magnitudes than short-dated contracts, gives a greatly enhanced fit.
Classification Basic Research, General Concepts and History of Economics; Economic Statistics, Econometrics, Business Informatics
Method basic research
Free Keywords Commodity options; Commodity derivatives; Jump diffusion; Mean reversion
Document language English
Publication Year 2008
Page/Pages p. 181-200
Journal Quantitative Finance, 8 (2008) 2
Status Postprint; peer reviewed
Licence PEER Licence Agreement (applicable only to documents from PEER project)