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Price Impacts of Imperfect Collateralization

Author

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  • Kenichiro Shiraya

    (The University of Tokyo)

  • Akihiko Takahashi

    (The University of Tokyo)

Abstract

This paper studies impacts of imperfect collateralization on derivatives values. Firstly, we present a general framework for the analysis in a multi-dimensional diffusion setting, and then calclate pre-default values of forwards and options for the numerical experiments. In particular, we investigate no collateral posting and timelagged collateral posting cases under a stochastic volatility model for the underlying asset prices and stochastic interest and hazard rate models for the risk-free rate and default intensities. We also derive an approximation for the density function of the CVA (Credit Value Adjustment) in the valuation of forward contract with bilateral counter party risk. Moreover, we allow a stochastic collateral asset value to depend not only on the underlying contract values, but also on other asset prices such as a currency different from the payment currency of the underlying contract. Finally, we also examine the effect of correlations on basket option values with stochastic volatility and stochastic hazard rate models.

Suggested Citation

  • Kenichiro Shiraya & Akihiko Takahashi, 2014. "Price Impacts of Imperfect Collateralization," CARF F-Series CARF-F-355, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Nov 2015.
    • Handle: RePEc:cfi:fseres:cf355
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    File URL: https://www.carf.e.u-tokyo.ac.jp/old/pdf/workingpaper/fseries/F355.pdf
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    References listed on IDEAS

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    1. Damiano Brigo & Andrea Pallavicini & Vasileios Papatheodorou, 2011. "Arbitrage-Free Valuation Of Bilateral Counterparty Risk For Interest-Rate Products: Impact Of Volatilities And Correlations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 773-802.
    2. Kenichiro Shiraya & Akihiko Takahashi, 2014. "Pricing Multiasset Cross‐Currency Options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(1), pages 1-19, January.
    3. Masaaki Fujii & Akihiko Takahashi, 2012. "Collateralized CDS and Default Dependence -Implications for the Central Clearing," CARF F-Series CARF-F-281, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
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    Cited by:

    1. Masaaki Fujii, 2015. "Optimal Position Management for a Market Maker with Stochastic Price Impacts," CIRJE F-Series CIRJE-F-963, CIRJE, Faculty of Economics, University of Tokyo.

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