Working Paper: NBER ID: w12744
Authors: Anders B. Trolle; Eduardo S. Schwartz
Abstract: We conduct a comprehensive analysis of unspanned stochastic volatility in commodity markets in general and the crude-oil market in particular. We present model-free results that strongly suggest the presence of unspanned stochastic volatility in the crude-oil market. We then develop a tractable model for pricing commodity derivatives in the presence of unspanned stochastic volatility. The model features correlations between innovations to futures prices and volatility, quasi-analytical prices of options on futures and futures curve dynamics in terms of a low-dimensional affine state vector. The model performs well when estimated on an extensive panel data set of crude-oil futures and options.
Keywords: Stochastic Volatility; Commodity Derivatives; Risk Management
JEL Codes: G13
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| volatility is predominantly unspanned by futures contracts (G13) | significant portion of volatility risk cannot be hedged through futures trading (G13) |
| dominant unspanned stochastic volatility factor (C58) | large common variations in regression residuals across different option maturities (C29) |
| futures prices are influenced by three factors (G13) | correlations between innovations in these factors (C10) |
| volatility may be partially spanned (C58) | volatility remains largely unspanned (C58) |
| model performs well in fitting futures prices and options (G13) | reinforces the claim that volatility is largely unspanned (C58) |