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Fair Bilateral Prices In Bergman’S Model With Exogenous Collateralization

Author

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  • TIANYANG NIE

    (School of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China)

  • MAREK RUTKOWSKI

    (School of Mathematics and Statistics, University of Sydney, Sydney, Camperdown NSW 2006, Australia)

Abstract

We examine the pricing and hedging of general contracts in an extension of the market model proposed by [B-1995]. We study both problems from the perspectives of the hedger and the counterparty with arbitrary initial endowments. We derive inequalities satisfied by unilateral prices of a contract and we give the range for its fair bilateral prices. Our study hinges on results for backward stochastic differential equations (BSDEs) driven by multi-dimensional continuous martingales obtained in Nie & Rutkowski (2014b). We also derive the pricing partial differential equations (PDEs) for path-independent contingent claims of European style in a Markovian framework.

Suggested Citation

  • Tianyang Nie & Marek Rutkowski, 2015. "Fair Bilateral Prices In Bergman’S Model With Exogenous Collateralization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-26, November.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:07:n:s021902491550048x
    DOI: 10.1142/S021902491550048X
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Bergman, Yaacov Z, 1995. "Option Pricing with Differential Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 8(2), pages 475-500.
    4. Damiano Brigo & Agostino Capponi & Andrea Pallavicini & Vasileios Papatheodorou, 2011. "Collateral Margining in Arbitrage-Free Counterparty Valuation Adjustment including Re-Hypotecation and Netting," Papers 1101.3926, arXiv.org.
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    Cited by:

    1. Marek Rutkowski & Matthew Bickersteth, 2021. "Pricing and Hedging of SOFR Derivatives under Differential Funding Costs and Collateralization," Papers 2112.14033, arXiv.org.
    2. Damiano Brigo & Cristin Buescu & Marco Francischello & Andrea Pallavicini & Marek Rutkowski, 2018. "Risk-neutral valuation under differential funding costs, defaults and collateralization," Papers 1802.10228, arXiv.org.

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