A Consistent Framework for Funding and Credit Valuation Adjustments

Summary

The paper develops a risk-neutral pricing framework for counterparty credit risk that incorporates funding and margin costs. It allows for asymmetric collateral and funding rates, as well as externally specified liquidity policies and hedging strategies. The framework also addresses liquidity risk from re-hypothecation and complications in evaluating close-out amounts, while accommodating margining and netting practices associated with standard market documentation.

Its main result is a bilateral pricing equation that combines credit valuation adjustment, debt valuation adjustment, margining, and funding costs. The equation is recursive, which makes a simple additive funding valuation adjustment difficult to introduce. The authors instead express the pricing problem as iterative relationships that can be solved with standard least-squares Monte Carlo methods. Examples show how earlier results about funding and counterparty risk, including discounting curves, can be derived from the broader setup. The excerpt does not give numerical case results or implementation details, and practical conclusions depend on the chosen policies and contractual assumptions.

Key ideas

• The framework incorporates funding, margining, and counterparty credit risk in risk-neutral pricing.
• It permits asymmetric funding and collateral rates and flexible margining and netting assumptions.
• Re-hypothecation liquidity risk and close-out amount evaluation are included.
• A recursive bilateral pricing equation combines credit, debt, margin, and funding effects.
• The authors propose solving iterative relationships with least-squares Monte Carlo.

Tags

# Funding Valuation Adjustment: a consistent framework including CVA, DVA, collateral,netting rules and re-hypothecation


# Funding Valuation Adjustment: a consistent framework including CVA, DVA, collateral,netting rules and re-hypothecation









In this paper we describe how to include funding and margining costs into a risk-neutral pricing framework for counterparty credit risk. We consider realistic settings and we include in our models the common market practices suggested by the ISDA documentation without assuming restrictive constraints on margining procedures and close-out netting rules. In particular, we allow for asymmetric collateral and funding rates, and exogenous liquidity policies and hedging strategies. Re-hypothecation liquidity risk and close-out amount evaluation issues are also covered. We define a comprehensive pricing framework which allows us to derive earlier results on funding or counterparty risk. Some relevant examples illustrate the non trivial settings needed to derive known facts about discounting curves by starting from a general framework and without resorting to ad hoc hypotheses. Our main result is a bilateral collateralized counterparty valuation adjusted pricing equation, which allows to price a deal while taking into account credit and debt valuation adjustments along with margining and funding costs in a coherent way. We find that the equation has a recursive form, making the introduction of an additive funding valuation adjustment difficult. Yet, we can cast the pricing equation into a set of iterative relationships which can be solved by means of standard least-square Monte Carlo techniques.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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