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A Tractable Framework for Option Pricing with Dynamic Market Maker Inventory and Wealth

Published online by Cambridge University Press:  19 July 2019

Mathieu Fournier Open the ORCID record for Mathieu Fournier [Opens in a new window]  and
Kris Jacobs
Mathieu Fournier*
Affiliation:
Fournier, [email protected], HEC Montréal
Kris Jacobs
Affiliation:
Jacobs, [email protected], University of Houston
*
Fournier (corresponding author), [email protected]
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Abstract

We develop a tractable dynamic model of an index option market maker with limited capital. We solve for the variance risk premium and option prices as a function of the asset dynamics and market maker option holdings and wealth. The market maker absorbs end users’ positive demand and requires a more negative variance risk premium when she incurs losses. We estimate the model using returns, options, and inventory and find that it performs well, especially during the financial crisis. The restrictions imposed by nested existing reduced-form stochastic-volatility models are strongly rejected in favor of the model with a market maker.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 55 , Issue 4 , June 2020 , pp. 1117 - 1162
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2019

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Footnotes

For helpful comments we thank an anonymous referee, Daniel Andrei, David Bates, Peter Christoffersen, Julien Cujean, Ian Dew-Becker, Christian Dorion, Redouane Elkamhi, Wayne Ferson, Bruno Feunou, Jean-Sébastien Fontaine, Pascal François, Christian Gouriéroux, Amit Goyal, Ruslan Goyenko, Michael Hasler, Alexandre Jeanneret, Bryan Kelly, Aytek Malkhozov, Tom McCurdy, Dmitriy Muravyev, Chayawat Ornthanalai, Stylianos Perrakis, Norman Schüerhoff, Masahiro Watanabe, Jason Wei, and Alan White; seminar participants at the Bank of Canada, HEC Lausanne/Swiss Finance Institute, HEC Montréal, and Rotman; conference participants at the American Finance Association (AFA) meeting in San Francisco, the Northern Finance Association (NFA) meeting in Ottawa, Canadian Derivatives Institute (CDI), and IFM2; and market makers at the Chicago Board Options Exchange (CBOE). A previous version of this article was circulated as “Inventory Risk, Market Maker Wealth, and the Variance Risk Premium: Theory and Evidence.”

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