Abstract
The Schwartz (J Finance 52(3):923–973, 1997) two factor model serves as a benchmark for pricing commodity contracts, futures and options. It is normally calibrated to fit the term-structure of a range of future contracts with varying maturities. In this paper, we investigate the effects on parameter estimates, if the model is fitted to prices of options, with varying maturities and strikes instead of futures, as is commonly done. The use of option prices rather than futures in the calibration leads to non-linearities, which the standard Kalman filter approach is unable to cope with. To overcome these issues, we use the extended Kalman Filter. We find that some parameters sensitively depend on the choice of strikes of the corresponding options, and are different from those estimates obtained from using futures prices. This effect is analogue to varying implied volatilities in the Black–Scholes model. This realization is important, as the use of ill-fitted models for pricing options in the Schwartz (1997) framework may cause traders to bear serious financial losses.
Highlights
Crude oil is without doubt one of the most important commodities, strongly tied to industrial and economic growth
The Schwartz (J Finance 52(3):923–973, 1997) two factor model serves as a benchmark for pricing commodity contracts, futures and options
We investigate the effects on parameter estimates, if the model is fitted to prices of options, with varying maturities and strikes instead of futures, as is commonly done
Summary
Crude oil is without doubt one of the most important commodities, strongly tied to industrial and economic growth. Our paper expands on Schwartz (1997) and Hilliard and Reis (1998) as such as that we estimate the implied spot price and convenience yield of the underlying commodity from options rather than futures. We use the extended Kalman-Filter and prices of European call options on WTI crude oil futures to estimate the Schwartz (1997) model. The motivation for this lies in the fact that option prices carry far more information on the volatility structure of the underlying asset than futures do. Empirical results and conclusions will be discussed in the last section
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