A model-free approach to multivariate option pricing
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A model-free approach to multivariate option pricing Carole Bernard1,2
· Oleg Bondarenko3 · Steven Vanduffel2
Accepted: 5 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We propose a novel model-free approach to extract a joint multivariate distribution, which is consistent with options written on individual stocks as well as on various available indices. To do so, we first use the market prices of traded options to infer the risk-neutral marginal distributions for the stocks and the linear combinations given by the indices and then apply a new combinatorial algorithm to find a compatible joint distribution. Armed with the joint distribution, we can price general path-independent multivariate options. Keywords Multivariate option pricing · Rearrangement algorithm · Risk-neutral joint distribution · Option-implied dependence · Entropy · Model uncertainty Mathematics Subject Classification C63 · C65 · G13
The authors gratefully acknowledge funding from the Canadian Derivatives Institute (formerly called IFSID) and the Global Risk Institute (GRI) for the related project“Inferring tail correlations from options prices”.
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Carole Bernard [email protected] Oleg Bondarenko [email protected] Steven Vanduffel [email protected]
1
Department of Accounting, Law and Finance, Grenoble Ecole de Management (GEM), Grenoble, France
2
Department of Economics and Political Sciences, Vrije Universiteit Brussel (VUB), Ixelles, Belgium
3
Department of Finance, University of Illinois at Chicago (UIC), Chicago, USA
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Introduction In this paper, we propose a novel model-free approach for pricing multivariate options. The approach is entirely driven by prices of existing options, which we use for inferring the risk-neutral joint distribution among the stocks. Pricing methods that appear in the literature typically amount to selecting a parametric multi-stock model that reflects salient features observed in financial markets (e.g., jumps, fat tails, tail dependence) and next calibrating it in a manner that renders it consistent with the prices of existing options. For instance, Cont and Deguest (2013) propose a mixture of models that can reproduce some set of multivariate options prices and individual options. Other approaches build on Lévy processes. However, while their application in univariate stock modeling is well understood, the multivariate setting still represents challenges. Issues include difficulties with their estimation (curse of dimensionality) and concerns about their ability to closely match dependence patterns observed in the data. Loregian et al. (2018) develop an efficient estimation methodology for a multivariate model driven by Lévy processes. The approach allows them to model a possibly complex dependence among assets, with different tail behaviors and jump structures for each stock; see also Ballotta and Bonfiglioli (2016). Other studies are conducted by Avellaneda and Boyer-Olson (2002) and Jourdain and Sbai (2012). The abo
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