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 / Cosso, Andrea; Marazzina, Daniele; Sgarra, Carlo. - In: STOCHASTICS. - ISSN 1744-2508. - STAMPA. - 87:(2015), pp. 518-536. [10.1080/17442508.2014.989525]
American option valuation in a stochastic volatility model with transaction costs
Cosso, Andrea;
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.