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Finance and Stochastics

Erschienen in:

01.04.2012

Singular risk-neutral valuation equations

verfasst von: Cristina Costantini, Marco Papi, Fernanda D’Ippoliti

Erschienen in: Finance and Stochastics | Ausgabe 2/2012

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Abstract

Many risk-neutral pricing problems proposed in the finance literature do not admit closed-form expressions and have to be dealt with by solving the corresponding partial integro-differential equation. Often, these PIDEs have singular diffusion matrices and coefficients that are not Lipschitz-continuous up to the boundary. In addition, in general, boundary conditions are not specified. In this paper, we prove existence and uniqueness of (continuous) viscosity solutions for linear PIDEs with all the above features, under a Lyapunov-type condition. Our results apply to European and Asian option pricing, in jump-diffusion stochastic volatility and path-dependent volatility models. We verify our Lyapunov-type condition in several examples, including the arithmetic Asian option in the Heston model.

Vorheriger Artikel Deterministic criteria for the absence of arbitrage in one-dimensional diffusion models

Nächster Artikel Strict local martingale deflators and valuing American call-type options

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Titel: Singular risk-neutral valuation equations
verfasst von: Cristina Costantini
Marco Papi
Fernanda D’Ippoliti
Publikationsdatum: 01.04.2012
Verlag: Springer-Verlag
Erschienen in: Finance and Stochastics / Ausgabe 2/2012
Print ISSN: 0949-2984
Elektronische ISSN: 1432-1122
DOI: https://doi.org/10.1007/s00780-011-0166-8

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