Collateral represents the tool of choice for mitigating Counterparty Credit Risk in the post 2008 market environment. However, the impact of its funding on the overall profitability of an institution, or a trade, can be difficult to assess. While OIS has emerged as the new proxy for the risk-free rate and the standard for collateral discounting, the fact remains that a multitude of funding rates dictated by collateral agreements are utilized across a portfolio.

In this Numerix Research Brief, Dr. Ion Mihai, Quantitative Analyst at Numerix, walks through a high-level explanation of the principles and logic behind the Numerix quantitative approach to Funding Value Adjustment, FVA. He discusses how the inclusion of multiple sources of funding—such as unsecured money market funding, collateral and repo— leads to a nonlinear partial differential equation (PDE), featuring multiple discounting rates. Solving this nonlinear PDE is a difficult numerical problem, which is why disposing of a practical approximate implementation methodology is as important as working on rigorous theoretical foundations.

Highlights include:

  • Our expansion upon Vladimir Piterbarg’s framework1 to develop a generic numerical methodology for computing FVA
  • How our approach allows the problem to be treated on a deal-by-deal basis, which easily enables the calculation to be parallelized
  • Pricing in a multi-rate economy
  • A fast approximated methodology for computing FVA

1 Vladimir Piterbarg (2010), “Funding beyond discounting: collateral agreements and derivatives pricing,” RISK, Feb. 

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