Dynamics between crude oil and equity markets under the risk-neutral measure

Abstract

This article investigates the time series relationship between equity and crude oil markets using option-implied risk-neutral moments. We recover daily time series of constant-maturity risk-neutral volatility (RNV), skewness and kurtosis using options data for the S&P 500 and WTI oil futures over the period January 1996 to October 2011. The transmission of shocks is analysed for each risk-neutral moment using a vector autoregression model where each market is represented by one equation. Impulse response functions and variance decompositions are recovered and analysed. Our contribution is to document the transmission of shocks measured through investor anticipations in both markets. Our results suggest the transmission of shocks measured through investor anticipations is different under the risk-neutral measure than under the physical measure previously studied in the literature. Shocks to equity market RNV and skewness are transmitted to oil RNVand skewness while the reverse is not observed. However, shocks to risk-neutral kurtosis in one market do not affect the other market. The crystallized changes in investor anticipations in equity markets are eventually passed on to oil markets.

Keywords:

• risk-neutral moments
• options
• vector autoregression
• oil markets
• equity markets

JEL Classification:

• G13
• G14

Notes

¹ Since our results suggest that the equity market leads the oil futures market under the risk-neutral measure, it is reasonable to assume that the equity market will also lead the oil spot market.

² We set the contemporaneous impact of an oil shock on the stock market to be zero. As a robustness check, we also estimate the model with the opposite restriction, where the impact of contemporaneous shocks of equities on oil is set to zero. The results being similar, only the latter are reported.

³ To conserve space, IRF and variance decompositions are presented only for the 1-month maturity, as IRFs for other maturities are similar, but with somewhat lower variance decomposition for longer maturities (9 and 12 months).

⁴ In the interest of brevity, we present only the IRF and variance decompositions for the 12-month maturity as the other maturities have similar IRF with somewhat lower variance decompositions.

⁵ In the interest of brevity, we present only the IRF and variance decompositions for the 1-month maturity as the other maturities have similar results.