Ionut Florescu, Maria C. Mariani, Indranil SenGupta
Abstract:
In a realistic market with transaction costs, the option pricing problem
is known to lead to solving nonlinear partial differential equations even
in the simplest model. The nonlinear term in these partial differential
equations (PDE) reflects the presence of transaction costs.
In this article we consider an underlying general stochastic volatility model.
In this case the market is incomplete and the option price is not unique.
Under a particular market completion assumption where we use a traded proxy
for the volatility, we obtain a non-linear PDE whose solution provides the
option price in the presence of transaction costs. This PDE is studied and
under suitable regularity conditions, we prove the existence of strong
solutions of the problem.
Submitted November 20, 2013. Published July 30, 2014.
Math Subject Classifications: 35R09, 91G20, 91G80.
Key Words: Stochastic volatility models; transaction costs models;
nonlinear PDEs; financial market.
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Ionut Florescu Financial Engineering Division and Hanlon Financial Systems Lab Stevens Institute of Technology Castle Point on Hudson Hoboken, NJ 07030, USA email: ifloresc@stevens.edu |
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Maria C. Mariani Department of Mathematical Sciences University of Texas at El Paso, Bell Hall 124 El Paso, TX 79968-0514, USA email: mcmariani@utep.edu |
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Indranil SenGupta Department of Mathematics North Dakota State University NDSU Dept # 2750, Minard Hall 408E12 Fargo, ND 58108-6050, USA email: indranil.sengupta@ndsu.edu |
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