Credit Value Adjustment (CVA) Introduction

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Credit value adjustment (CVA) is the market price of counterparty credit risk that has become a central part of counterparty credit risk management. This presentation answers several fundamental questions: what is CVA? Why does CVA become important? How can one compute CVA? You find more presentations at http://www.finpricing.com/paperList.html

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Credit Value Adjustment CVA Introduction Alex Yang FinPricing http://www.finpricing.com

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CVA Introduction Summary ◆ CVA History ◆ CVA Definition ◆ Risk Free Valuation ◆ Risky Valuation

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CVA Introduction CVA History ◆ Current market practice ◆ Discounting using the LIBOR or risk-free curves ◆ Using risk-free value for pricing hedging PL ◆ Real counterparty reality ◆ Having different credit qualities from LIBOR ◆ Having risk of default ◆ ISA 39 International Accounting Standard ◆ Requiring CVA in 2000 mandatory ◆ Finance and Accounting owning CVA ◆ Receiving a little attention in the beginning ◆ Becoming significant risk after financial crises

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CVA Introduction CVA Definition ◆ Definition CVA Risk free value – True risky value ◆ Benefits ◆ Quantifying counterparty risk as a single PL number ◆ Dynamically managing pricing and hedging counterparty risk ◆ Notes ◆ CVA is a topic of valuation and requires accurate pricing and risk- neutral measure ◆ Risk-free valuation is what we use every day. Risky valuation is less explored and less transparent

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CVA Introduction Risk-Free Valuation ◆ The risk-free valuation is what brokers quote or what trading systems or models normally report. ◆ A simple example to illustrate  A zero coupon bond paying X at T ◆ The risk-free value where r is risk-free interest rate and is risk-free discount factor X T D rT exp X 0 V F   

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CVA Introduction Risky Valuation ◆ Default Modeling ◆ Structural models  Studying default based on capital structure of a firm ◆ Reduced form models  Characterizing default as a jump Poisson process ◆ Market practitioners prefer the reduced form models due to  Mathematical tractability  Consistency with market observations as risk-neutral default probabilities can be backed out from bond prices and CDS spreads

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CVA Introduction Risky Valuation Continuously Defaultable ◆ The same simple example: a zero coupon bond paying X at T ◆ The risk value where r is risk-free interest rate and s is credit spread is risk adjusted discounting factor ◆ CVA by defintion

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CVA Introduction Risky Valuation Discrete Defaultable ◆ Assumption ◆ default may happen only at the payment date ◆ At time T the bond either survives with payoff X or defaults with payoff where is the recovery rate ◆ Risk value where p is default probability and q1-p is the survival probability ◆ CVA

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Thanks You can find more details at http://www.finpricing.com/lib/cva.pdf

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