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A BSDE approach to fair bilateral pricing under endogenous collateralization

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  • Tianyang Nie
  • Marek Rutkowski

Abstract

Our previous results are extended to the case of the margin account, which may depend on the contract's value for the hedger and/or the counterparty. The present work generalizes also the papers by Bergman (1995), Mercurio (2013) and Piterbarg (2010). Using the comparison theorems for BSDEs, we derive inequalities for the unilateral prices and we give the range for its fair bilateral prices. We also establish results yielding the link to the market model with a single interest rate. In the case where the collateral amount is negotiated between the counterparties, so that it depends on their respective unilateral values, the backward stochastic viability property studied by Buckdahn et al. (2000) is used to derive the bounds on fair bilateral prices.

Suggested Citation

  • Tianyang Nie & Marek Rutkowski, 2014. "A BSDE approach to fair bilateral pricing under endogenous collateralization," Papers 1412.2453, arXiv.org.
    • Handle: RePEc:arx:papers:1412.2453
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    References listed on IDEAS

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    1. Tomasz R. Bielecki & Marek Rutkowski, 2014. "Valuation and Hedging of Contracts with Funding Costs and Collateralization," Papers 1405.4079, arXiv.org, revised Dec 2014.
    2. 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.
    3. Tianyang Nie & Marek Rutkowski, 2014. "Fair and profitable bilateral prices under funding costs and collateralization," Papers 1410.0448, arXiv.org, revised Dec 2014.
    4. 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.
    5. 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.
    6. Tianyang Nie & Marek Rutkowski, 2014. "Fair bilateral prices in Bergman's model," Papers 1410.0673, arXiv.org, revised Dec 2014.
    7. 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. Damiano Brigo & Marco Francischello & Andrea Pallavicini, 2015. "Invariance, existence and uniqueness of solutions of nonlinear valuation PDEs and FBSDEs inclusive of credit risk, collateral and funding costs," Papers 1506.00686, arXiv.org, revised Nov 2015.

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