City Research Online

Abstract

We develop a joint model for the S&P500 and the VIX indices with the aim of extracting forward looking information on the correlation between the two markets. We achieve this by building the model on time changed L´evy processes, deriving closed analytical expressions for relevant quantities directly from the joint characteristic function, and exploiting the market quotes of options on both indices. We perform a piecewise joint calibration to the option prices to ensure the highest level of precision within the limits of the availability of quotes in the dataset and their liquidity. Using the calibrated parameters, we are able to quantify the leverage effect along the term structure of the VIX options and corresponding VIX futures. We illustrate the model using market data on S&P500 options and both futures and options on the VIX.

Publication Type:	Article
Additional Information:	This article has been published in a revised form in Frontiers of Mathematical Finance 10.3934/fmf.2025005. This version is free to download for private research and study only. Not for redistribution, re-sale or use in derivative works.
Publisher Keywords:	Levy processes; time changes; implied correlation; option pricing
Subjects:	H Social Sciences > HG Finance
Departments:	Bayes Business School Bayes Business School > Finance
SWORD Depositor:	Symplectic Administrator

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