A multi-factor model for improved commodity pricing: calibration and an application to the oil market

We present a new approach to commodity pricing that enhances accuracy by integrating four distinct risk factors: the spot price, stochastic volatility, convenience yield, and stochastic interest rates. We build on Yan [Valuation of commodity derivatives in a new multi-factor model. Rev. Deriv. Res., 2002, 5, 251–271], the only model to our knowledge that incorporates all four sources of risk, and extend it by adding a more flexible correlation structure that captures state-dependent co-movements and time-varying risk premia. A further contribution is the explicit inclusion of the stochastic interest-rate factor within a unified Kalman-filter framework, which allows us to jointly filter the state variables and estimate model parameters using both commodity and bond market data. An empirical analysis of crude-oil futures shows that our four-factor model captures the complex dynamics of the futures term structure and consistently outperforms existing benchmarks.