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Gap Risk KVA and Repo Pricing: An Economic Capital Approach in the Black-Scholes-Merton Framework

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  • Wujiang Lou

Abstract

Although not a formal pricing consideration, gap risk or hedging errors are the norm of derivatives businesses. Starting with the gap risk during a margin period of risk of a repurchase agreement (repo), this article extends the Black-Scholes-Merton option pricing framework by introducing a reserve capital approach to the hedging error's irreducible variability. An extended partial differential equation is derived with two new terms for expected gap loss and economic capital charge, leading to the gap risk economic value adjustment and capital valuation adjustment (KVA) respectively. Practical repo pricing formulae is obtained showing that the break-even repo rate decomposes into cost of fund and economic capital charge in KVA. At zero haircut, a one-year term repo on main equities could command a capital charge as large as 50 basis points for a 'BBB' rated borrower.

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  • Wujiang Lou, 2016. "Gap Risk KVA and Repo Pricing: An Economic Capital Approach in the Black-Scholes-Merton Framework," Papers 1604.05406, arXiv.org, revised Oct 2016.
    • Handle: RePEc:arx:papers:1604.05406
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Wujiang Lou, 2015. "Liability-side Pricing of Swaps and Coherent CVA and FVA by Regression/Simulation," Papers 1512.07340, arXiv.org.
    3. Wujiang Lou, 2015. "Coherent CVA and FVA with Liability Side Pricing of Derivatives," Papers 1510.07199, arXiv.org.
    4. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    5. Andrew Green & Chris Kenyon, 2014. "KVA: Capital Valuation Adjustment," Papers 1405.0515, arXiv.org, revised Oct 2014.
    6. 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.
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