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Adapting the CVA model to Leland's framework

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  • P. Amster
  • A. P. Mogni

Abstract

We consider the framework proposed by Burgard and Kjaer (2011) that derives the PDE which governs the price of an option including bilateral counterparty risk and funding. We extend this work by relaxing the assumption of absence of transaction costs in the hedging portfolio by proposing a cost proportional to the amount of assets traded and the traded price. After deriving the nonlinear PDE, we prove the existence of a solution for the corresponding initial-boundary value problem. Moreover, we develop a numerical scheme that allows to find the solution of the PDE by setting different values for each parameter of the model. To understand the impact of each variable within the model, we analyze the Greeks of the option and the sensitivity of the price to changes in all the risk factors.

Suggested Citation

  • P. Amster & A. P. Mogni, 2018. "Adapting the CVA model to Leland's framework," Papers 1802.04837, arXiv.org.
    • Handle: RePEc:arx:papers:1802.04837
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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. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    3. 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.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    5. Indranil SenGupta, 2014. "Option Pricing with Transaction Costs and Stochastic Interest Rate," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(5), pages 399-416, November.
    6. Damiano Brigo & Kyriakos Chourdakis, 2009. "Counterparty Risk For Credit Default Swaps: Impact Of Spread Volatility And Default Correlation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 1007-1026.
    7. Boyle, Phelim P & Vorst, Ton, 1992. "Option Replication in Discrete Time with Transaction Costs," Journal of Finance, American Finance Association, vol. 47(1), pages 271-293, March.
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