In the present paper we analyse the American option valuation problem in a stochastic volatility model when transaction costs are taken into account. We shall show that it can be formulated as a singular stochastic optimal control problem, proving the existence and uniqueness of the viscosity solution for the associated Hamilton-Jacobi-Bellman partial differential equation. Moreover, after performing a dimensionality reduction through a suitable choice of the utility function, we shall provide a numerical example illustrating how American options prices can be computed in the present modelling framework.

American option valuation in a stochastic volatility model with transaction costs / A. Cosso, D. Marazzina, C. Sgarra. - In: STOCHASTICS. - ISSN 1744-2508. - 87:3(2015), pp. 518-536. [10.1080/17442508.2014.989525]

American option valuation in a stochastic volatility model with transaction costs

A. Cosso
Primo
;
2015

Abstract

In the present paper we analyse the American option valuation problem in a stochastic volatility model when transaction costs are taken into account. We shall show that it can be formulated as a singular stochastic optimal control problem, proving the existence and uniqueness of the viscosity solution for the associated Hamilton-Jacobi-Bellman partial differential equation. Moreover, after performing a dimensionality reduction through a suitable choice of the utility function, we shall provide a numerical example illustrating how American options prices can be computed in the present modelling framework.
American options; transaction costs; stochastic volatility; viscosity solutions
Settore MAT/06 - Probabilita' e Statistica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/931986
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