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Liability-side Pricing of Swaps and Coherent CVA and FVA by Regression/Simulation

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  • Wujiang Lou

Abstract

An uncollateralized swap hedged back-to-back by a CCP swap is used to introduce FVA. The open IR01 of FVA, however, is a sure sign of risk not being fully hedged, a theoretical no-arbitrage pricing concern, and a bait to lure market risk capital, a practical business concern. By dynamically trading the CCP swap, with the liability-side counterparty provides counterparty exposure hedge and swap funding, we find that the uncollateralized swap can be fully replicated, leaving out no IR01 leakage. The fair value of the swap is obtained by applying to swap's net cash flows a discount rate switching to counterparty's bond curve if the swap is a local asset or one's own curve if a liability, and the total valuation adjustment is the present value of cost of funding the risk-free price discounted at the same switching rate. FVA is redefined as a liquidity or funding basis component of total valuation adjustment, coherent with CVA, the default risk component. A Longstaff-Schwartz style least-square regression and simulation is introduced to compute the recursive fair value and adjustments. A separately developed finite difference scheme is used to test and find regression necessary to decouple the discount rate switch. Preliminary results show the impact of counterparty risk to swap hedge ratios, swap bid/ask spreads, and valuation adjustments, and considerable errors of calculating CVA by discounting cash flow or potential future exposure.

Suggested Citation

  • Wujiang Lou, 2015. "Liability-side Pricing of Swaps and Coherent CVA and FVA by Regression/Simulation," Papers 1512.07340, arXiv.org.
    • Handle: RePEc:arx:papers:1512.07340
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    References listed on IDEAS

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    1. Hubner, Georges, 2001. "The analytic pricing of asymmetric defaultable swaps," Journal of Banking & Finance, Elsevier, vol. 25(2), pages 295-316, February.
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    Cited by:

    1. Wujiang Lou, 2015. "MVA Transfer Pricing," Papers 1512.07337, arXiv.org, revised Jul 2016.
    2. 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.

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