A Stochastic Volatility Model for Crude Oil Futures Curves and the Pricing of Calendar Spread Options
AbstractWe introduce a multi-factor stochastic volatility model based on the CIR/Heston stochastic volatility process. In order to capture the Samuelson effect displayed by commodity futures contracts, we add expiry-dependent exponential damping factors to their volatility coefficients. The pricing of single underlying European options on futures contracts is straightforward and can incorporate the volatility smile or skew observed in the market. We calculate the joint characteristic function of two futures contracts in the model and use the two-dimensional FFT method of Hurd and Zhou (SIFIN 2010) to price calendar spread options. The model leads to stochastic correlation between the returns of two futures contracts. We illustrate the distribution of this correlation in an example.
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