VIX vs. SPX Options: Skewness, Term Structure, and Hedging Implications

VIX index options have become the second most traded contracts on the CBOE, surpassed only by S&P 500 (SPX) options. However, unlike SPX options, where the term structure of volatility has been extensively studied, the volatility term structure of VIX options has received far less attention. Reference [1] fills this gap by examining the term structure of VIX options and their role in hedging.

The authors pointed out,

In equity and variance swap options, it is well known that implied volatilities exhibit convexity (i.e., smile) over strikes. In our VIX option data, the smile is actually a concave frown for the most part of our sample, and particularly so when VIX is low. When VIX is high, it surprisingly changes to a convex smile. Even more surprisingly, our model replicates this empirical phenomenon.

We show that VIX options variations are not necessarily spanned by SPX options as a PCA decomposition shows that VIX options returns contain variation not seen in SPX options. The model also replicates the time-varying nature of the hedging relationship between SPX options, the underlying SPX index, VIX futures, and VIX options. In regressing SPX put option changes onto changes in these variables, we find that VIX options are nearly uncorrelated with SPX options in low volatility periods while the correlation spikes in high volatility periods. Our model explains this through essentially time varying factor loadings: when volatility is low, ATM SPX options depend primarily on cash flow news, while ATM VIX options depend on volatility and jump arrival intensity. In high volatility periods, the correlations increase, and VIX call options can serve as important hedging instruments for SPX puts.

In summary, some notable features of VIX options are,

• While the implied Black-Scholes volatility for SPX options is always a convex function of strike, VIX options behave differently, their shape shifts from concave in normal times to convex during high-volatility periods.
• The distribution of VIX returns is also markedly different from that of equities: VIX exhibits a strong right skew, far more pronounced than the left skew typically seen in SPX returns.
• VIX options display a downward-sloping term structure, i.e. longer-dated contracts have lower implied volatilities than shorter ones.
• Shocks to the implied volatility of volatility (VVIX) are positively, but not perfectly, correlated with VIX itself, suggesting that VIX option prices include components beyond just the VIX level.
• During calm markets, VIX calls don’t show a meaningful correlation with SPX puts and offer limited value for hedging. However, in turbulent times, VIX calls significantly reduce hedging errors, highlighting how VIX options (or SPX puts) can become valuable hedging instruments during periods of market stress.

This is a very important contribution, as it helps better understand the relationships within the SPX and VIX complex.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Eraker, B., and A. Yang. 2022. The Price of Higher Order Catastrophe Insurance: The Case of VIX Options. Journal of Finance 77, no. 6: 3289–3337.

Originally Published Here: VIX vs. SPX Options: Skewness, Term Structure, and Hedging Implications

source https://harbourfronts.com/vix-vs-spx-options-skewness-term-structure-hedging-implications/