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Arbitrage-Free Pricing Of Derivatives In Nonlinear Market Models

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  • Tomasz R. Bielecki
  • Igor Cialenco
  • Marek Rutkowski

Abstract

The objective of this paper is to provide a comprehensive study no-arbitrage pricing of financial derivatives in the presence of funding costs, the counterparty credit risk and market frictions affecting the trading mechanism, such as collateralization and capital requirements. To achieve our goals, we extend in several respects the nonlinear pricing approach developed in El Karoui and Quenez (1997) and El Karoui et al. (1997), which was subsequently continued in Bielecki and Rutkowski (2015).

Suggested Citation

  • Tomasz R. Bielecki & Igor Cialenco & Marek Rutkowski, 2017. "Arbitrage-Free Pricing Of Derivatives In Nonlinear Market Models," Papers 1701.08399, arXiv.org, revised Apr 2018.
    • Handle: RePEc:arx:papers:1701.08399
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    References listed on IDEAS

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    1. Shige Peng & Xiaoming Xu, 2009. "BSDEs with random default time and their applications to default risk," Papers 0910.2091, arXiv.org.
    2. Claudio Albanese & Simone Caenazzo & Stéphane Crépey, 2016. "Capital Valuation Adjustment and Funding Valuation Adjustment," Working Papers hal-01285363, HAL.
    3. Tomasz R. Bielecki & Monique Jeanblanc & Marek Rutkowski, 2006. "Hedging of Credit Derivatives in Models with Totally Unexpected Default," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 2, pages 35-100, World Scientific Publishing Co. Pte. Ltd..
    4. Roxana Dumitrescu & Marie-Claire Quenez & Agnès Sulem, 2015. "Game options in an imperfect market with default," Working Papers hal-01243603, HAL.
    5. Roxana Dumitrescu & Marie-Claire Quenez & Agn`es Sulem, 2015. "Game options in an imperfect market with default," Papers 1511.09041, arXiv.org, revised Jul 2017.
    6. Quenez, Marie-Claire & Sulem, Agnès, 2013. "BSDEs with jumps, optimization and applications to dynamic risk measures," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3328-3357.
    7. Andrea Pallavicini & Daniele Perini & Damiano Brigo, 2012. "Funding, Collateral and Hedging: uncovering the mechanics and the subtleties of funding valuation adjustments," Papers 1210.3811, arXiv.org, revised Dec 2012.
    8. Ioannis Karatzas & (*), S. G. Kou, 1998. "Hedging American contingent claims with constrained portfolios," Finance and Stochastics, Springer, vol. 2(3), pages 215-258.
    9. Stéphane Crépey & Shiqi Song, 2016. "Counterparty risk and funding: immersion and beyond," Finance and Stochastics, Springer, vol. 20(4), pages 901-930, October.
    10. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    11. Damiano Brigo & Andrea Pallavicini, 2014. "Nonlinear consistent valuation of CCP cleared or CSA bilateral trades with initial margins under credit, funding and wrong-way risks," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-60.
    12. Bergman, Yaacov Z, 1995. "Option Pricing with Differential Interest Rates," The Review of Financial Studies, Society for Financial Studies, vol. 8(2), pages 475-500.
    13. Tianyang Nie & Marek Rutkowski, 2016. "A BSDE approach to fair bilateral pricing under endogenous collateralization," Finance and Stochastics, Springer, vol. 20(4), pages 855-900, October.
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    Cited by:

    1. Edward Kim & Tianyang Nie & Marek Rutkowski, 2018. "Arbitrage-free pricing of American options in nonlinear markets," Papers 1804.10753, arXiv.org, revised Jul 2018.
    2. Damiano Brigo & Cristin Buescu & Marco Francischello & Andrea Pallavicini & Marek Rutkowski, 2022. "Nonlinear Valuation with XVAs: Two Converging Approaches," Mathematics, MDPI, vol. 10(5), pages 1-31, March.
    3. Yining Ding & Ruyi Liu & Marek Rutkowski, 2024. "Cross-Currency Basis Swaps Referencing Backward-Looking Rates," Papers 2410.08477, arXiv.org.
    4. Junbeom Lee & Chao Zhou, 2021. "Binary funding impacts in derivative valuation," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 242-278, January.
    5. Tianyang Nie & Edward Kim & Marek Rutkowski, 2018. "Arbitrage-Free Pricing of Game Options in Nonlinear Markets," Papers 1807.05448, arXiv.org.
    6. Marek Rutkowski & Matthew Bickersteth, 2021. "Pricing and Hedging of SOFR Derivatives under Differential Funding Costs and Collateralization," Papers 2112.14033, arXiv.org.
    7. Jun Sekine & Akihiro Tanaka, 2020. "Notes on Backward Stochastic Differential Equations for Computing XVA," Papers 2006.02173, arXiv.org.
    8. Weijie Pang & Stephan Sturm, 2020. "XVA Valuation under Market Illiquidity," Papers 2011.03543, arXiv.org.
    9. Alessio Calvelli, 2022. "No-Arbitrage Pricing, Dynamics and Forward Prices of Collateralized Derivatives," Papers 2208.08746, arXiv.org, revised Jun 2024.

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