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Joint valuation of SPX and VIX options by GARCH models with bad and good environments
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王
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DOI：10.1016/j.jbankfin.2026.107719.png)
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Abstract
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We develop a GARCH model inspired by the bad environment-good environment (BEGE) framework and apply it to the joint valuation of SPX and volatility index (VIX) options. Our empirical analysis using S&P 500 index returns reveals that the bad volatility component is significantly more volatile than the good volatility component and accounts for the majority of total volatility. Regarding SPX and VIX option pricing, we find that the BEGE model outperforms several competing models that involve two volatility components, both in-sample and out-of-sample. Moreover, we decompose the risk premiums (equity and variance) into their good and bad components. The good components are small and positive, with upward-sloping term structures. The bad components dominate the total premiums, with the bad component of the equity (variance) risk premium being positive (negative) and exhibiting an upward-sloping (downward-sloping) term structure. During periods of very high volatility, the shape of the term structure tends to invert.
Keywords:
GARCH model
BEGE framework
SPX options
VIX options
volatility decomposition
Journal
J
IF:
3.8
Papers:
65
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