Extreme-Strike Comparisons and Structural Bounds for SPX and VIX Options
Andrew Papanicolaou
TL;DR
This paper investigates the deep connection between SPX and VIX options markets, using model-free formulas to compare implied volatilities and analyze tail risk hedging strategies.
Contribution
It introduces a model-free approach to quantify the relationship between SPX and VIX options, highlighting the role of extreme-strike asymptotics and providing comparative analysis across models.
Findings
High-strike VIX calls hedge SPX tail risk effectively
SPX options reflect VIX extreme-strike asymptotics
Model comparisons reveal consistent implied volatility patterns
Abstract
This article explores the relationship between the SPX and VIX options markets. High-strike VIX call options are used to hedge tail risk in the SPX, which means that SPX options are a reflection of the extreme-strike asymptotics of VIX options, and vice versa. This relationship can be quantified using moment formulas in a model-free way. Comparisons are made between VIX and SPX implied volatilities along with various examples of stochastic volatility models.
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Taxonomy
TopicsStochastic processes and financial applications · Capital Investment and Risk Analysis · Financial Risk and Volatility Modeling