Bilateral Credit Risk Valuation

Interest rate swap (IRS) is one of the most popular financial derivatives. In the market, IRS’s are quoted irrespective of credit ratings of counterparties. In another words, they are considered as default-free. The valuation of default-free IRS’s under a term structure of interest rates is a classical exercise. However, swap contracts are traded over-the-counter (OTC) and are not backed by the guarantee of a clearing corporation or an exchange. As a consequence, each party is exposed to the credit risk (default risk). Historical experience shows that credit risk often leads to significant losses. Therefore, one should incorporate the cost of the counterparty risk into the swap price.

Pricing defaultable derivatives or pricing the counterparty credit risk is a relatively new area of derivatives modeling and trading. Credit value adjustment (CVA) allows us to quantify counterparty credit risk as a single, measurable Profit & Loss number. By definition, CVA is the difference between the risk-free trade value and the true (or risky or defaultable) trade value that takes into account the possibility of counterparty’s default. Commonly, the CVA is not paid as a lump-sum upfront premium, but rather is structured into a funding spread. The risk-free trade value is what brokers quote or what trading systems or models normally report. The defaultable trade value, however, is a relatively less explored and less transparent area, which is the main challenge and core theme for credit risk adjustment.

IRS is a typical bilateral contingent contract that can be either an asset or a liability to each party during the life of the contract. Unlike the unilateral defaultable claim valuation problems that have been studied extensively by many authors, the valuation of bilateral contingent claims is still lacking convincing mechanism. The problem is mainly caused by the asymmetric credit qualities and the asymmetric default settlement rules.

Sundaresan (1991), Longstaff and Schwartz (1993), and Tang and Li (2007) simplify the problem by considering the IRS as a simple exchange of loans (receivable parts and payable parts). It is inappropriate to value a defaultable IRS by pricing the default risk of the promised gross payment from each party separately and then adding the two together. Because the promised cash flow exchange in an IRS is always netted. Another simplification consists of taking into account the presence of one risky counterparty only, as in Li (1998) and Arvanities and Gregory (2001). These approaches overlook the presence of bilateral default risk.

The first study on asymmetric defaultable IRS is conducted by Duffie and Huang (1996). They use a short rate interest rate model combined with a reduced-form default model and lead to numerical approximations by solving a recursive integral. Even the authors admit that it is a substantial complexity solution. Hubner (2001) extends the work carried out by Duffie and Huang (1996) and gets a closed-form solution by introducing a one-dimensional state variable X that can be thought of as a ratio of the market value of the firm’s assets. The author, however, does not show how to calibrate the state variable and not even provide a simple example. In general, these proposed models are not practical enough to use.

• osf asset back
• Zenodo fx hedge
• OSF hw vol
• zenodo cash hedge
• pubpub asian quanto
• github gic pooling