Seasonal Stochastic Volatility: Implications for the Pricing of Commodity Options

Abstract

Many commodity markets contain a strong seasonal component not only at the price level, but also in volatility. In this paper, the importance of seasonal behavior in the volatility for the pricing of commodity options is analyzed. We propose a seasonally varying long-run mean variance process that is capable of capturing empirically observed patterns. Semi-closedform option valuation formulas are derived. We then empirically study the impact of the proposed seasonal stochastic volatility model on the pricing accuracy of natural gas futures options traded at the New York Mercantile Exchange (NYMEX) and corn futures options traded at the Chicago Board of Trade (CBOT). Our results demonstrate that allowing stochastic volatility to fluctuate seasonally significantly reduces pricing errors for these contracts.

Seasonal Stochastic Volatility and Correlation Together with the Samuelson Effect in Commodity Futures Markets

“…This parametric form for θ is used in Back et al (2011). There is no closed form expression for θT (λ).…”

“…They conclude that a volatility with seasonality is an important feature when valuing options on futures in these markets. Back et al (2011) also study a futures-based model with seasonal stochastic volatility, which is essentially the Heston (1993) stochastic volatility model with deterministic, seasonal mean-reversion level in the square-root process followed by the variance. Schmitz et al (2013) study calendar spread options in agricultural grain markets relying on a joint Heston model for the two underlying futures contracts.…”