Pricing of long-dated commodity derivatives: Do stochastic interest rates matter?

Abstract

Does modelling stochastic interest rates, beyond stochastic volatility, improve pricing performance on long-dated commodity derivatives? To answer this question, we consider futures price models for commodity derivatives that allow for stochastic volatility and stochastic interest rates and a correlation structure between the underlying variables. We examine the empirical pricing performance of these models on pricing long-dated crude oil derivatives.Estimating the model parameters from historical crude oil futures prices and option prices, we find that stochastic interest rate models improve pricing performance on long-dated crude oil derivatives, when the interest rate volatility is relatively high. Furthermore, increasing the model dimensionality does not tend to improve the pricing performance on long-dated crude oil option prices, but it matters for long-dated futures prices. We also find empirical evidence for a negative correlation between crude oil futures prices and interest rates that contributes to improving fit to long-dated crude oil option prices.

Interest rate risk in long‐dated commodity options positions: To hedge or not to hedge?

“…The hedging of long-dated commodity derivatives is studied using the futures pricing model of Cheng et al (2017), which accommodates stochastic volatility, stochastic interest rates, and a full correlation structure. This model improves pricing performance for long-dated crude oil futures (compared to deterministic interest rate specifications), especially over periods of high volatility in commodity and interest rate markets, see Cheng et al (2017). For completeness, we summarise the model specifications here.…”

“…The i o satisfy complex-valued Ricatti ordinary differential equations, see Cheng et al (2017) for full details. For the estimation applications, the market price of risk and the market price of volatility risk, namely, ϖ i and ϖ i σ , respectively, are specified by…”

“…The empirical study on hedging long-dated commodity derivatives is conducted using data from the most liquid of the commodity derivatives markets, the crude oil market. This application requires a model that provides a good fit to market data, thus we employ the multidimensional stochastic volatility and stochastic interest rate model proposed by Cheng et al (2017), as outlined in Section 2.1. In Section 2.2, the hedge ratios for a variety of hedging schemes have been obtained by using the factor-hedging methodology.…”

“…In contrast, most of the literature is restricted to spot price models, which cannot fit well the term structure of the futures curve and/or cannot accommodate all these dimensions of risk. 4 Cheng et al (2017) have empirically demonstrated that this stochastic volatility-stochastic interest rate model improves pricing performance on long-dated crude oil derivative prices, and thus provides a "good" fit to market data. Alexander and Kaeck (2012) provide empirical evidence on the importance of the model calibration for hedging performance of stochastic volatility models in FTSE 100 options.…”

“…This paper conducts an extensive empirical study using crude oil derivatives, arguably the most important and most liquid commodity derivatives market. 3 To this end, the futures pricing model by Cheng, Nikitopoulos, and Schlögl (2017) is used, since it integrates commodity, volatility, and interest rate risk, making it well suited to compute hedge ratios for these risks. In contrast, most of the literature is restricted to spot price models, which cannot fit well the term structure of the futures curve and/or cannot accommodate all these dimensions of risk.…”