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Characterization of Market Models in the Presence of Traded Vanilla and Barrier Options

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  • Peter Spoida

Abstract

We characterize the set of market models when there are a finite number of traded Vanilla and Barrier options with maturity $T$ written on the asset $S$. From a probabilistic perspective, our result describes the set of joint distributions for $(S_T, \sup_{u \leq T} S_u)$ when a finite number of marginal law constraints on both $S_T$ and $\sup_{u \leq T} S_u$ is imposed. An extension to the case of multiple maturities is obtained. Our characterization requires a decomposition of the call price function and once it is obtained, we can explicitly express certain joint probabilities in this model. In order to obtain a fully specified joint distribution we discuss interpolation methods.

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  • Peter Spoida, 2014. "Characterization of Market Models in the Presence of Traded Vanilla and Barrier Options," Papers 1411.4193, arXiv.org.
    • Handle: RePEc:arx:papers:1411.4193
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    References listed on IDEAS

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    1. Forde, Martin, 2011. "A diffusion-type process with a given joint law for the terminal level and supremum at an independent exponential time," Stochastic Processes and their Applications, Elsevier, vol. 121(12), pages 2802-2817.
    2. Mark H. A. Davis & David G. Hobson, 2007. "The Range Of Traded Option Prices," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 1-14, January.
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    Cited by:

    1. Stefan Gerhold & I. Cetin Gulum, 2016. "Consistency of option prices under bid-ask spreads," Papers 1608.05585, arXiv.org, revised Jul 2019.

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