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Option Pricing with Transaction Costs and Stochastic Interest Rate

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  • Indranil SenGupta

Abstract

In the case when transaction costs are associated with trading assets the option pricing problem is known to lead to solving nonlinear partial differential equations even when the underlying asset is modelled using a simple geometric Brownian motion. The nonlinear term in the resulting PDE corresponds to the presence of transaction costs. We generalize this model to a stochastic one-factor interest rate model. We show that the model follows a nonlinear parabolic type partial differential equation. Under certain assumption we prove the existence of classical solution for this model.

Suggested Citation

  • Indranil SenGupta, 2014. "Option Pricing with Transaction Costs and Stochastic Interest Rate," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(5), pages 399-416, November.
    • Handle: RePEc:taf:apmtfi:v:21:y:2014:i:5:p:399-416
    DOI: 10.1080/1350486X.2014.881263
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    Cited by:

    1. Indranil Sengupta, 2016. "Generalized Bn–S Stochastic Volatility Model For Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-23, March.
    2. Semere Habtemicael & Indranil SenGupta, 2016. "Pricing variance and volatility swaps for Barndorff-Nielsen and Shephard process driven financial markets," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 1-35, December.
    3. Semere Habtemicael & Indranil Sengupta, 2016. "Pricing Covariance Swaps For Barndorff–Nielsen And Shephard Process Driven Financial Markets," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 1-32, September.
    4. Shantanu Awasthi & Indranil SenGupta, 2020. "First exit-time analysis for an approximate Barndorff-Nielsen and Shephard model with stationary self-decomposable variance process," Papers 2006.07167, arXiv.org, revised Jan 2021.
    5. P. Amster & A. P. Mogni, 2018. "Adapting the CVA model to Leland's framework," Papers 1802.04837, arXiv.org.
    6. Yipeng Yang & Allanus Tsoi, 2016. "A Level Set Analysis and A Nonparametric Regression on S&P 500 Daily Return," IJFS, MDPI, vol. 4(1), pages 1-24, February.
    7. 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).
    8. Pablo Amster & Andres P. Mogni, 2017. "On a pricing problem for a multi-asset option with general transaction costs," Papers 1704.02036, arXiv.org, revised Sep 2018.

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