An Analytical Expression for Credit Valuation Adjustment Pricing with Wrong-Way Risk

Kelin Pan; Chandra Khandrika

doi:doi:10.11648/j.eco.20211003.14

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An Analytical Expression for Credit Valuation Adjustment Pricing with Wrong-Way Risk

Kelin Pan, Chandra Khandrika

Published in Economics (Volume 10, Issue 3)

Received: 23 May 2021 Accepted: 9 June 2021 Published: 6 September 2021

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Abstract

Recently, financial institutions were required to provide the financial derivatives instrument level credit valuation adjustment (CVA) by the new accounting standard. CVA trading desks are facing difficulties to calculate a netting-set level CVA with wrong-way risk (WWR) since the dynamics of the exposures and probability of default (PD) are separated and calculated by different counterparty credit risk (CCR) computing systems. Another difficult work is that the netting-set level CVA mixed the pricing models for all trades under a netting-set. It is significant to develop a new CVA model that is based on the credit adjustment to the existing pricing model under one risk-neutral framework. This paper presents the work on CVA with WWR under the credit deterioration dynamics in both normal and stressed economic conditions. In terms of the double-correlation structure that is constructed based on the Gaussian latent variable models we propose an analytical expression of CVA for the fundamental financial derivatives such as futures or forwards contracts. The double-correlation structure captures the market- and asset-credit correlations. The proposed CVA pricing framework is based on the credit deterioration dynamics rather than default dynamics. The credit deterioration index (CDI) is defined as the limit of the credit deterioration variable and calculated using the rating agency credit rating transition data. The proposed CVA with WWR model is a function of the correlations, CDI, counterparty probability of default, loss given default, interest rate and volatility of the traded derivatives. The market- and asset-credit correlation parameters are calibrated to either the normal or stressed market. Under the stressed market, the scenario design, shock variable selection and shock magnitude are discussed. The numerical results show that the CVA is an increasing function of the market-credit correlation and a decreasing function of the credit rating. The stressed CVA is about four times higher than the normal CVA.

Published in	Economics (Volume 10, Issue 3)
DOI	10.11648/j.eco.20211003.14
Page(s)	94-104
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Wrong-Way Risk, Credit Deterioration Dynamics, Market-Credit Correlation, Stressed CVA, Gaussian Latent Variable Models

References

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[2]	Redon C. (2006), 'Wrong Way Risk Modelling', Risk, April issue, pp. 90-95.
[3]	Brigo D. and Pallavicini A. (2006), 'Counterparty Risk and Contingent CDS Valuation Under Correlation Between Interest-Rates and Default', SSRN Electronic Journal, August, available at DOI: 10.2139/ssrn.926067.
[4]	Brigo D., Chourdakis K. and Bakkar I. (2008) 'Counterparty Risk Valuation for Energy-Commodities Swaps', Fitch Solutions, available at https://arxiv.org/abs/0901.1099
[5]	Pykhtin M. and Rosen D. (2010) 'Pricing Counterparty Risk at the Trade Level and Credit Valuation Adjustment Allocations', The Journal of Credit Risk, Vol. 6, No. 4, pp. 3-38.
[6]	Cespedes J., Herrero J., Rosen D. and Saunders D. (2010) 'Effective Modeling of Wrong Way Risk, Counterparty Credit Risk Capital, and Alpha in Basel II', The Journal of Risk Model Validation, Vol. 4, No. 1, pp. 71-98.
[7]	Rosen D. and Saunders D. (2012) 'CVA the Wrong Way', Journal of Risk Management in Financial Institutions, Vol. 5, No. 3, pp. 252-272.
[8]	Hull J. and White A. (2012) 'CVA and Wrong-Way Risk', Financial Analysts Journal, Vol. 68, No. 5, pp. 58-69.
[9]	Ghamami S. and Goldberg L. (2014) 'Stochastic Intensity Models of Wrong Way Risk: Wrong Way CVA Need Not Exceed Independent CVA', The Journal of Derivatives, Vol. 21, No. 3, pp. 24-35.
[10]	Lipton A. and Sepp A. (2009) 'Credit Value Adjustment for Credit Default Swaps via the Structural Default Model', The Journal of Credit Risk, Vol. 5, No. 2, pp. 123-146.
[11]	Pang T., Chen W. and Li L. (2015) 'CVA Wrong Way Risk Multiplier Decomposition and Efficient CVA Curve', Journal of Risk Management in Financial Institutions, Vol. 8, No. 4, pp. 390-404.
[12]	Chung T-K. and Gregory J. (2019) 'CVA Wrong-Way Risk: Calibration Using a Quanto CDS Basis', Risk. net, 02 July 2019.
[13]	Pan K. (2018) 'CVA Pricing for Commodities with WWR', Cutting Edge Energy Risk, July issue 2018.
[14]	Pan K. and Khandrika C. (2019) 'Credit Valuation Adjustment Wrong Way Risk in a Gaussian Copula Model', The Journal of Credit Risk, Vol. 15, No. 4, pp. 43-57.
[15]	Gregory J. (2013) 'Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets', The Fourth Edition, Wiley, West Sussex, UK.
[16]	Gregory J. (2015) 'The xVA Challenge', The Third Edition, Wiley, West Sussex, UK.
[17]	Brigo D. and F. Mercurio (2006) 'Interest Rate Models - Theory and Practice with Smile, Inflation and Credit', The second Ed., Springer.
[18]	Board of Governors of the Federal Reserve System (2020) 'Capital Assessments and Stress Testing Information Collection Q&As', September, available at https://www.federalreserve.gov/publications/files/fr-y-14qas.pdf
[19]	Li D. (2000) 'On Default Correlation: a Copula Function Approach', The Journal of Fixed Income, Vol. 9, No 4, pp. 43-54. available at https://doi.org/10.2469/faj.v68.n5.6
[20]	Vasicek, O. (2002) 'The Distribution of Loan Portfolio Value', Risk, Vol. 15, No. 12, 160-162.
[21]	O'Kane D. (2008) 'Modelling Single-name and Multi-name Credit Derivatives', Wiley, New Jersey.
[22]	Pan K. (2017) 'An Analytical Expression for Bivariate Normal Distribution', SSRN Electronic Journal, February 2017, available at https://ssrn.com/abstract=2924071
[23]	Vazza D. and Kraemer N. (2021) '2020 Annual Global Corporate Default and Rating Transition Study', RatingsDirect S&P, April 7 2021, available at https://www.maalot.co.il/Publications/TS20210408160139.PDF

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Kelin Pan, Chandra Khandrika. (2021). An Analytical Expression for Credit Valuation Adjustment Pricing with Wrong-Way Risk. Economics, 10(3), 94-104. https://doi.org/10.11648/j.eco.20211003.14

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Kelin Pan; Chandra Khandrika. An Analytical Expression for Credit Valuation Adjustment Pricing with Wrong-Way Risk. Economics. 2021, 10(3), 94-104. doi: 10.11648/j.eco.20211003.14

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Kelin Pan, Chandra Khandrika. An Analytical Expression for Credit Valuation Adjustment Pricing with Wrong-Way Risk. Economics. 2021;10(3):94-104. doi: 10.11648/j.eco.20211003.14

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@article{10.11648/j.eco.20211003.14,
  author = {Kelin Pan and Chandra Khandrika},
  title = {An Analytical Expression for Credit Valuation Adjustment Pricing with Wrong-Way Risk},
  journal = {Economics},
  volume = {10},
  number = {3},
  pages = {94-104},
  doi = {10.11648/j.eco.20211003.14},
  url = {https://doi.org/10.11648/j.eco.20211003.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.eco.20211003.14},
  abstract = {Recently, financial institutions were required to provide the financial derivatives instrument level credit valuation adjustment (CVA) by the new accounting standard. CVA trading desks are facing difficulties to calculate a netting-set level CVA with wrong-way risk (WWR) since the dynamics of the exposures and probability of default (PD) are separated and calculated by different counterparty credit risk (CCR) computing systems. Another difficult work is that the netting-set level CVA mixed the pricing models for all trades under a netting-set. It is significant to develop a new CVA model that is based on the credit adjustment to the existing pricing model under one risk-neutral framework. This paper presents the work on CVA with WWR under the credit deterioration dynamics in both normal and stressed economic conditions. In terms of the double-correlation structure that is constructed based on the Gaussian latent variable models we propose an analytical expression of CVA for the fundamental financial derivatives such as futures or forwards contracts. The double-correlation structure captures the market- and asset-credit correlations. The proposed CVA pricing framework is based on the credit deterioration dynamics rather than default dynamics. The credit deterioration index (CDI) is defined as the limit of the credit deterioration variable and calculated using the rating agency credit rating transition data. The proposed CVA with WWR model is a function of the correlations, CDI, counterparty probability of default, loss given default, interest rate and volatility of the traded derivatives. The market- and asset-credit correlation parameters are calibrated to either the normal or stressed market. Under the stressed market, the scenario design, shock variable selection and shock magnitude are discussed. The numerical results show that the CVA is an increasing function of the market-credit correlation and a decreasing function of the credit rating. The stressed CVA is about four times higher than the normal CVA.},
 year = {2021}
}

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TY  - JOUR
T1  - An Analytical Expression for Credit Valuation Adjustment Pricing with Wrong-Way Risk
AU  - Kelin Pan
AU  - Chandra Khandrika
Y1  - 2021/09/06
PY  - 2021
N1  - https://doi.org/10.11648/j.eco.20211003.14
DO  - 10.11648/j.eco.20211003.14
T2  - Economics
JF  - Economics
JO  - Economics
SP  - 94
EP  - 104
PB  - Science Publishing Group
SN  - 2376-6603
UR  - https://doi.org/10.11648/j.eco.20211003.14
AB  - Recently, financial institutions were required to provide the financial derivatives instrument level credit valuation adjustment (CVA) by the new accounting standard. CVA trading desks are facing difficulties to calculate a netting-set level CVA with wrong-way risk (WWR) since the dynamics of the exposures and probability of default (PD) are separated and calculated by different counterparty credit risk (CCR) computing systems. Another difficult work is that the netting-set level CVA mixed the pricing models for all trades under a netting-set. It is significant to develop a new CVA model that is based on the credit adjustment to the existing pricing model under one risk-neutral framework. This paper presents the work on CVA with WWR under the credit deterioration dynamics in both normal and stressed economic conditions. In terms of the double-correlation structure that is constructed based on the Gaussian latent variable models we propose an analytical expression of CVA for the fundamental financial derivatives such as futures or forwards contracts. The double-correlation structure captures the market- and asset-credit correlations. The proposed CVA pricing framework is based on the credit deterioration dynamics rather than default dynamics. The credit deterioration index (CDI) is defined as the limit of the credit deterioration variable and calculated using the rating agency credit rating transition data. The proposed CVA with WWR model is a function of the correlations, CDI, counterparty probability of default, loss given default, interest rate and volatility of the traded derivatives. The market- and asset-credit correlation parameters are calibrated to either the normal or stressed market. Under the stressed market, the scenario design, shock variable selection and shock magnitude are discussed. The numerical results show that the CVA is an increasing function of the market-credit correlation and a decreasing function of the credit rating. The stressed CVA is about four times higher than the normal CVA.
VL  - 10
IS  - 3
ER  -

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Author Information

Kelin Pan

Citibank, Tampa, USA
Chandra Khandrika

Citibank, New York, USA

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Kelin Pan, Chandra Khandrika. (2021). An Analytical Expression for Credit Valuation Adjustment Pricing with Wrong-Way Risk. Economics, 10(3), 94-104. https://doi.org/10.11648/j.eco.20211003.14

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Kelin Pan; Chandra Khandrika. An Analytical Expression for Credit Valuation Adjustment Pricing with Wrong-Way Risk. Economics. 2021, 10(3), 94-104. doi: 10.11648/j.eco.20211003.14

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Kelin Pan, Chandra Khandrika. An Analytical Expression for Credit Valuation Adjustment Pricing with Wrong-Way Risk. Economics. 2021;10(3):94-104. doi: 10.11648/j.eco.20211003.14

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@article{10.11648/j.eco.20211003.14,
  author = {Kelin Pan and Chandra Khandrika},
  title = {An Analytical Expression for Credit Valuation Adjustment Pricing with Wrong-Way Risk},
  journal = {Economics},
  volume = {10},
  number = {3},
  pages = {94-104},
  doi = {10.11648/j.eco.20211003.14},
  url = {https://doi.org/10.11648/j.eco.20211003.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.eco.20211003.14},
  abstract = {Recently, financial institutions were required to provide the financial derivatives instrument level credit valuation adjustment (CVA) by the new accounting standard. CVA trading desks are facing difficulties to calculate a netting-set level CVA with wrong-way risk (WWR) since the dynamics of the exposures and probability of default (PD) are separated and calculated by different counterparty credit risk (CCR) computing systems. Another difficult work is that the netting-set level CVA mixed the pricing models for all trades under a netting-set. It is significant to develop a new CVA model that is based on the credit adjustment to the existing pricing model under one risk-neutral framework. This paper presents the work on CVA with WWR under the credit deterioration dynamics in both normal and stressed economic conditions. In terms of the double-correlation structure that is constructed based on the Gaussian latent variable models we propose an analytical expression of CVA for the fundamental financial derivatives such as futures or forwards contracts. The double-correlation structure captures the market- and asset-credit correlations. The proposed CVA pricing framework is based on the credit deterioration dynamics rather than default dynamics. The credit deterioration index (CDI) is defined as the limit of the credit deterioration variable and calculated using the rating agency credit rating transition data. The proposed CVA with WWR model is a function of the correlations, CDI, counterparty probability of default, loss given default, interest rate and volatility of the traded derivatives. The market- and asset-credit correlation parameters are calibrated to either the normal or stressed market. Under the stressed market, the scenario design, shock variable selection and shock magnitude are discussed. The numerical results show that the CVA is an increasing function of the market-credit correlation and a decreasing function of the credit rating. The stressed CVA is about four times higher than the normal CVA.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - An Analytical Expression for Credit Valuation Adjustment Pricing with Wrong-Way Risk
AU  - Kelin Pan
AU  - Chandra Khandrika
Y1  - 2021/09/06
PY  - 2021
N1  - https://doi.org/10.11648/j.eco.20211003.14
DO  - 10.11648/j.eco.20211003.14
T2  - Economics
JF  - Economics
JO  - Economics
SP  - 94
EP  - 104
PB  - Science Publishing Group
SN  - 2376-6603
UR  - https://doi.org/10.11648/j.eco.20211003.14
AB  - Recently, financial institutions were required to provide the financial derivatives instrument level credit valuation adjustment (CVA) by the new accounting standard. CVA trading desks are facing difficulties to calculate a netting-set level CVA with wrong-way risk (WWR) since the dynamics of the exposures and probability of default (PD) are separated and calculated by different counterparty credit risk (CCR) computing systems. Another difficult work is that the netting-set level CVA mixed the pricing models for all trades under a netting-set. It is significant to develop a new CVA model that is based on the credit adjustment to the existing pricing model under one risk-neutral framework. This paper presents the work on CVA with WWR under the credit deterioration dynamics in both normal and stressed economic conditions. In terms of the double-correlation structure that is constructed based on the Gaussian latent variable models we propose an analytical expression of CVA for the fundamental financial derivatives such as futures or forwards contracts. The double-correlation structure captures the market- and asset-credit correlations. The proposed CVA pricing framework is based on the credit deterioration dynamics rather than default dynamics. The credit deterioration index (CDI) is defined as the limit of the credit deterioration variable and calculated using the rating agency credit rating transition data. The proposed CVA with WWR model is a function of the correlations, CDI, counterparty probability of default, loss given default, interest rate and volatility of the traded derivatives. The market- and asset-credit correlation parameters are calibrated to either the normal or stressed market. Under the stressed market, the scenario design, shock variable selection and shock magnitude are discussed. The numerical results show that the CVA is an increasing function of the market-credit correlation and a decreasing function of the credit rating. The stressed CVA is about four times higher than the normal CVA.
VL  - 10
IS  - 3
ER  -

Copy | Download