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Fair bilateral prices in Bergman's model

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  • Tianyang Nie
  • Marek Rutkowski

Abstract

Bielecki and Rutkowski (2014) introduced and studied a generic nonlinear market model, which includes several risky assets, multiple funding accounts and margin accounts. In this paper, we examine the pricing and hedging of contract both from the perspective of the hedger and the counterparty with arbitrary initial endowments. We derive inequalities for unilateral prices and we give the range for either fair bilateral prices or bilaterally profitable prices. We also study the monotonicity of a unilateral price with respect to the initial endowment. Our study hinges on results for BSDE driven by continuous martingales obtained in Nie and Rutkowski (2014), but we also derive the pricing PDEs for path-independent contingent claims of European style in a Markovian framework.

Suggested Citation

  • Tianyang Nie & Marek Rutkowski, 2014. "Fair bilateral prices in Bergman's model," Papers 1410.0673, arXiv.org, revised Dec 2014.
    • Handle: RePEc:arx:papers:1410.0673
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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. 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. Tianyang Nie & Marek Rutkowski, 2014. "Fair and profitable bilateral prices under funding costs and collateralization," Papers 1410.0448, arXiv.org, revised Dec 2014.
    2. Tianyang Nie & Marek Rutkowski, 2014. "A BSDE approach to fair bilateral pricing under endogenous collateralization," Papers 1412.2453, arXiv.org.

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