Bilateral Counterparty Risk Under Funding Constraints—part I: Pricing

Crépey, Stéphane

doi:10.1111/mafi.12004

Cited by 133 publications

(106 citation statements)

References 22 publications

(26 reference statements)

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“…If the trade is collateralized, we need to impose even further restrictions as to how the collateral is linked to the price of the tradeV . It should be noted here that funding DVA (as referred to in the previous section) is similar to the DVA2 in Hull and White [28] and the concept of "windfall funding benefit at own default" in Crépey [22,23]. In practice, however, funds transfer pricing and similar operations conducted by banks' treasuries clearly weaken the link between FVA and this source of DVA.…”

Section: Theorem 1 (Generalized Valuation Equation)mentioning

confidence: 97%

“…This PDE could be solved directly as in Crépey [22]. However, if we apply the Feynman-Kac theorem again-this time going from the pre-default PDE to the valuation expectation-and integrate by parts, we arrive at the following result Theorem 3 decomposes the deal priceV into three intuitive terms.…”

Section: Where V T Is the Price Of The Deal When There Is No Credit Rmentioning

confidence: 99%

“…For instance, Crépey [21][22][23] refers to LVA as the liquidity component (i.e., net of credit) of the funding valuation adjustment.…”

Section: Where V T Is the Price Of The Deal When There Is No Credit Rmentioning

confidence: 99%

“…Morini and Prampolini [31], Fries [25] and Castagna [19] consider basic implications of funding in presence of default risk. However, the most comprehensive attempts to develop a consistent valuation framework are those of Burgard and Kjaer [16,17], Crépey [21][22][23], Crépey et al [24], Pallavicini et al [33,34], and Brigo et al [13,14].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinearity Valuation Adjustment

Brigo

Liu

Pallavicini

et al. 2016

Innovations in Derivatives Markets

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We develop a consistent, arbitrage-free framework for valuing derivative trades with collateral, counterparty credit risk, and funding costs. Credit, debit, liquidity, and funding valuation adjustments (CVA, DVA, LVA, and FVA) are simply introduced as modifications to the payout cash flows of the trade position. The framework is flexible enough to accommodate actual trading complexities such as asymmetric collateral and funding rates, replacement close-out, and re-hypothecation of posted collateral-all aspects which are often neglected. The generalized valuation equation takes the form of a forward-backward SDE or semi-linear PDE. Nevertheless, it may be recast as a set of iterative equations which can be efficiently solved by our proposed least-squares Monte Carlo algorithm. We implement numerically the case of an equity option and show how its valuation changes when including the above effects. In the paper we also discuss the financial impact of the proposed valuation framework and of nonlinearity more generally. This is fourfold: First, the valuation equation is only based on observable market rates, leaving the value of a derivatives transaction invariant to any theoretical risk-free rate. Secondly, the presence of funding costs makes the valuation problem a highly recursive and nonlinear one. Thus, credit and funding risks are non-separable in general, and despite common practice in banks, CVA, DVA, and FVA cannot be treated as purely additive adjustments without running the risk of double counting. To quantify the valuation error that can be attributed to double counting, we introduce a "nonlinearity valuation adjustment" (NVA) and show that its magnitude can be significant under asymmetric funding rates and replacement close-out at default. Thirdly, as trading parties cannot observe each others' liquidity policies nor their respective funding costs, the bilateral nature of a derivative price breaks down. The value of a trade to a counterparty will not be just the opposite of the value seen by the bank. Finally, valuation becomes aggregation-dependent and portfolio values cannot simply be added up. This has operational consequences for banks, calling for a holistic, consistent approach across trading desks and asset classes.

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Section: Theorem 1 (Generalized Valuation Equation)mentioning

confidence: 97%

Section: Where V T Is the Price Of The Deal When There Is No Credit Rmentioning

confidence: 99%

“…For instance, Crépey [21][22][23] refers to LVA as the liquidity component (i.e., net of credit) of the funding valuation adjustment.…”

Section: Where V T Is the Price Of The Deal When There Is No Credit Rmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinearity Valuation Adjustment

Brigo

Liu

Pallavicini

et al. 2016

Innovations in Derivatives Markets

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“…Current FVA-related literature treats funding costs as an input [BK11,BK12,MP11,Cré12a,Cré12b,PPB11,PPB12] that is usually constant ([PB13] is an exception), and always risk-neutral. Books specifically on liquidity [CF13] or from a Treasury point of view [Cho12] do not treat funding costs as constant, but do not cover funding optimization mathematically.…”

Section: Introductionmentioning

confidence: 99%

Regulatory-Optimal Funding

Kenyon

Green

2013

SSRN Journal

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Funding is a cost to trading desks that they see as an exogenous input. Current FVA-related literature reflects this by also taking funding costs as an exogenous input, usually constant, and always risk-neutral. However, this funding curve is the output from the point of view of the Treasury department of a bank. The Treasury must consider Regulatory-required liquidity buffers, and both risk-neutral (Q) and physical measures (P). We describe the Treasury funding problem and optimize against both measures, using the Regulatory requirement as a constraint. We develop theoretically optimal strategies for Q and P measures, and then demonstrate a combined approach in four markets (USD, JPY, EUR, GBP). Since we deal with physical measures we develop appropriate statistical tests, and demonstrate highly significant (p<0.00001), out-of-sample, improvements on hedged funding with a combined approach achieving 44% to 71% of a perfect information criterion. Thus regulatory liquidity requirements change both the funding problem and funding costs.

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