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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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    1. Hammoudeh, Shawkat & McAleer, Michael, 2013. "Risk management and financial derivatives: An overview," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 109-115.
    2. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
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    5. McAleer, Michael & Jimenez-Martin, Juan-Angel & Perez-Amaral, Teodosio, 2013. "Has the Basel Accord improved risk management during the global financial crisis?," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 250-265.
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    8. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    Cited by:

    1. 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.
    2. Chadd B. Hunzinger & Coenraad C.A. Labuschagne, 2015. "Pricing a Collateralized Derivative Trade with a Funding Value Adjustment," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 8(1), pages 1-26, January.

    More about this item

    Keywords

    Tree model; Burgard and Kjaer model; Credit risky derivative; Cox; Ross and Rubinstein model; CVA; DVA; FVA;

    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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