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Nonlinear problems modeling stochastic volatility and transaction costs

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  • Maria C. Mariani
  • Indranil SenGupta

Abstract

The option pricing problem when the asset is driven by a stochastic volatility process and in the presence of transaction costs leads to solving a nonlinear partial differential equation (PDE). The nonlinear term in the PDE reflects the presence of transaction costs. Under a particular market completion assumption we derive the nonlinear PDE whose solution may be used to find the price of options. Under suitable conditions, we give an algorithmic scheme to obtain the solution of the problem by an iterative method. We prove theoretically the existence of strong solutions to the problem.

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  • Maria C. Mariani & Indranil SenGupta, 2012. "Nonlinear problems modeling stochastic volatility and transaction costs," Quantitative Finance, Taylor & Francis Journals, vol. 12(4), pages 663-670, April.
    • Handle: RePEc:taf:quantf:v:12:y:2012:i:4:p:663-670
    DOI: 10.1080/14697688.2012.664944
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    Cited by:

    1. Yan, Dong & Lin, Sha & Hu, Zhihao & Yang, Ben-Zhang, 2022. "Pricing American options with stochastic volatility and small nonlinear price impact: A PDE approach," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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