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The Cox, Ross and Rubinstein tree model which includes counterparty credit risk and funding costs

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  • Hunzinger, Chadd B.
  • Labuschagne, Coenraad C.A.

Abstract

The binomial asset pricing model of Cox, Ross and Rubinstein (CRR) is extensively used for the valuation of options. The CRR model is a discrete analog of the Black–Scholes–Merton (BSM) model. The 2008 credit crisis exposed the shortcomings of the oversimplified assumptions of the BSM model. Burgard and Kjaer extended the BSM model to include adjustments such as a credit value adjustment (CVA), a debit value adjustment (DVA) and a funding value adjustment (FVA). The aim of this paper is to extend the CRR model to include CVA, DVA and FVA and to prove that this extended CRR model coincides with the model that results from discretising the Burgard and Kjaer model. Our results are numerically implemented and we also show that as the number of time-steps increase in the derived tree structure model, the model converges to the model developed by Burgard and Kjaer.

Suggested Citation

  • Hunzinger, Chadd B. & Labuschagne, Coenraad C.A., 2014. "The Cox, Ross and Rubinstein tree model which includes counterparty credit risk and funding costs," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 200-217.
    • Handle: RePEc:eee:ecofin:v:29:y:2014:i:c:p:200-217
    DOI: 10.1016/j.najef.2014.06.002
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    References listed on IDEAS

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    6. 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.
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    8. Hull, John & White, Alan, 2013. "Credit Derivatives," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1363-1396, Elsevier.
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    Cited by:

    1. Li, Shuang & Peng, Cheng & Bao, Ying & Zhao, Yanlong, 2020. "Explicit expressions to counterparty credit exposures for Forward and European Option," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    2. Chadd B. Hunzinger & Coenraad C.A. Labuschagne, 2015. "Pricing a Collateralized Derivative Trade with a Funding Value Adjustment," JRFM, MDPI, vol. 8(1), pages 1-26, January.
    3. Lin, Shin-Hung & Huang, Hung-Hsi & Li, Sheng-Han, 2015. "Option pricing under truncated Gram–Charlier expansion," The North American Journal of Economics and Finance, Elsevier, vol. 32(C), pages 77-97.

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    More about this item

    Keywords

    Tree model; Burgard and Kjaer model; Credit risky derivative; Cox; Ross and Rubinstein model; CVA; DVA; FVA;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G01 - Financial Economics - - General - - - Financial Crises

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