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January  2017, 2: 7 doi: 10.1186/s41546-017-0019-2

Credit, funding, margin, and capital valuation adjustments for bilateral portfolios

Claudio Albanese 1,2, , Simone Caenazzo 1, and  Stéphane Crépey 3,

1 IMEX, London, UK;

2 CASS School of Business, London, UK;

3 LaMME, Univ Evry, CNRS, Université Paris-Saclay, 91037, Evry, France

Received  January 31, 2017 Revised  May 29, 2017 Published  December 2017

We apply to the concrete setup of a bank engaged into bilateral trade portfolios the XVA theoretical framework of Albanese and Crépey (2017), whereby so-called contra-liabilities and cost of capital are charged by the bank to its clients, on top of the fair valuation of counterparty risk, in order to account for the incompleteness of this risk. The transfer of the residual reserve credit capital from shareholders to creditors at bank default results in a unilateral CVA, consistent with the regulatory requirement that capital should not diminish as an effect of the sole deterioration of the bank credit spread. Our funding cost for variation margin (FVA) is defined asymmetrically since there is no benefit in holding excess capital in the future. Capital is fungible as a source of funding for variation margin, causing a material FVA reduction. We introduce a specialist initial margin lending scheme that drastically reduces the funding cost for initial margin (MVA). Our capital valuation adjustment (KVA) is defined as a risk premium, i.e. the cost of remunerating shareholder capital at risk at some hurdle rate.
Keywords: Counterparty risk, Credit valuation adjustment (CVA), Cost of funding variation margin (FVA), Cost of funding initial margin (MVA), Cost of capital (KVA).
Mathematics Subject Classification: 91B25;91B26;91B30;91G20;91G40.
Citation: Claudio Albanese, Simone Caenazzo, Stéphane Crépey. Credit, funding, margin, and capital valuation adjustments for bilateral portfolios. Probability, Uncertainty and Quantitative Risk, 2017, 2 (0) : 7-. doi: 10.1186/s41546-017-0019-2
References:
[1]

Albanese, C, Andersen, L:Accounting for OTC derivatives:Funding adjustments and the re-hypothecation option (2014). ssrn:2482955

[2]

Albanese, C, Andersen, L, Iabichino, S:FVA:Accounting and risk management (2015). Risk Magazine, February 64-68

[3]

Albanese, C, Bellaj, T, Gimonet, G:Pietronero G:Coherent global market simulations and securitization measures for counterparty credit risk. Quant Finance. 11(1), 1-20 (2011)

[4]

Albanese, C, Brigo, D, Oertel, F:Restructuring counterparty credit risk. Int. J. Theor. Appl. Finance. 16(2), 1350010 (29 pages) (2013)

[5]

Albanese, C, Crépey, S:XVA analysis from the balance sheet (2017). Working paper available at https://math.maths.univ-evry.fr/crepey. Accessed 7 June 2017

[6]

Andersen, L, Duffie, D, Song, Y:Funding value adjustments (2016). ssrn.2746010

[7]

Armenti, Y, Crépey, S:Central clearing valuation adjustment. SIAM J. Financial Math. 8, 274-313(2017a)

[8]

Armenti, Y, Crépey, S:XVA Metrics for CCP optimisation (2017b). Working paper available at https://math.maths.univ-evry.fr/crepey. Accessed 13 June 2017

[9]

Bichuch, M, Capponi, A, Sturm, S:Arbitrage-free XVA. Mathematical Finance (2016). Forthcoming(preprint version available at ssrn.2820257)

[10]

Bielecki, T, Rutkowski, M:Credit risk modelling:Intensity based approach. In:Jouini, E, Cvitanic, J, Musiela, M (eds.) Handbook in Mathematical Finance:Option Pricing, Interest Rates and Risk Management, pp. 399-457. Cambridge University Press, Cambridge (2001)

[11]

Bielecki, T, Rutkowski, M:Credit Risk:Modeling, Valuation and Hedging. Springer Finance, Berlin(2002)

[12]

Bielecki, TR, Rutkowski, M:Valuation and hedging of contracts with funding costs and collateralization.SIAM J. Financial Math. 6, 594-655 (2015)

[13]

Brigo, D, Capponi, A:Bilateral counterparty risk with application to CDSs (2008). arXiv:0812.3705, short version published later in 2010 in Risk Magazine Brigo, D, Pallavicini, A:Nonlinear consistent valuation of CCP cleared or CSA bilateral trades with initial margins under credit, funding and wrong-way risks. J. Financial Eng. 1, 1-60 (2014)

[14]

Burgard, C, Kjaer, M:Funding Strategies, Funding Costs. Risk Magazine, December, 82-87 (2013)

[15]

Collin-Dufresne, P, Goldstein, R, Hugonnier, J:A general formula for valuing defaultable securities.Econometrica. 72(5), 1377-1407 (2004)

[16]

Crépey, S:Bilateral counterparty risk under funding constraints. Part I:Pricing, followed by Part II:CVA. Math. Finance. 25(1), 1-50 (2015). First published online on 12 December 2012

[17]

Crépey, S, Élie, R, Sabbagh, W:When capital is a funding source:The XVA Anticipated BSDEs (2017). Working paper available at https://math.maths.univ-evry.fr/crepey

[18]

Crépey, S, Song, S:Counterparty risk and funding:Immersion and beyond. Finance Stochast. 20(4), 901-930 (2016)

[19]

Duffie, D, Huang, M:Swap rates and credit quality. J. Finance. 51, 921-950 (1996)

[20]

Duffie, D, Schroder, M, Skiadas, C:Recursive valuation of defaultable securities and the timing of resolution of uncertainty. Ann. Appl. Probab. 6(4), 1075-1090 (1996)

[21]

Kruse, T, Popier, A:BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration. Stochastics:Int. J. Probab. Stochast. Process. 88(4), 491-539 (2016)

[22]

Piterbarg, V:Funding beyond discounting:collateral agreements and derivatives pricing. Risk Mag. 2, 97-102 (2010)

[23]

Pykhtin, M:Model foundations of the Basel III standardised CVA charge. Risk Magazine (2012)

show all references

References:
[1]

Albanese, C, Andersen, L:Accounting for OTC derivatives:Funding adjustments and the re-hypothecation option (2014). ssrn:2482955

[2]

Albanese, C, Andersen, L, Iabichino, S:FVA:Accounting and risk management (2015). Risk Magazine, February 64-68

[3]

Albanese, C, Bellaj, T, Gimonet, G:Pietronero G:Coherent global market simulations and securitization measures for counterparty credit risk. Quant Finance. 11(1), 1-20 (2011)

[4]

Albanese, C, Brigo, D, Oertel, F:Restructuring counterparty credit risk. Int. J. Theor. Appl. Finance. 16(2), 1350010 (29 pages) (2013)

[5]

Albanese, C, Crépey, S:XVA analysis from the balance sheet (2017). Working paper available at https://math.maths.univ-evry.fr/crepey. Accessed 7 June 2017

[6]

Andersen, L, Duffie, D, Song, Y:Funding value adjustments (2016). ssrn.2746010

[7]

Armenti, Y, Crépey, S:Central clearing valuation adjustment. SIAM J. Financial Math. 8, 274-313(2017a)

[8]

Armenti, Y, Crépey, S:XVA Metrics for CCP optimisation (2017b). Working paper available at https://math.maths.univ-evry.fr/crepey. Accessed 13 June 2017

[9]

Bichuch, M, Capponi, A, Sturm, S:Arbitrage-free XVA. Mathematical Finance (2016). Forthcoming(preprint version available at ssrn.2820257)

[10]

Bielecki, T, Rutkowski, M:Credit risk modelling:Intensity based approach. In:Jouini, E, Cvitanic, J, Musiela, M (eds.) Handbook in Mathematical Finance:Option Pricing, Interest Rates and Risk Management, pp. 399-457. Cambridge University Press, Cambridge (2001)

[11]

Bielecki, T, Rutkowski, M:Credit Risk:Modeling, Valuation and Hedging. Springer Finance, Berlin(2002)

[12]

Bielecki, TR, Rutkowski, M:Valuation and hedging of contracts with funding costs and collateralization.SIAM J. Financial Math. 6, 594-655 (2015)

[13]

Brigo, D, Capponi, A:Bilateral counterparty risk with application to CDSs (2008). arXiv:0812.3705, short version published later in 2010 in Risk Magazine Brigo, D, Pallavicini, A:Nonlinear consistent valuation of CCP cleared or CSA bilateral trades with initial margins under credit, funding and wrong-way risks. J. Financial Eng. 1, 1-60 (2014)

[14]

Burgard, C, Kjaer, M:Funding Strategies, Funding Costs. Risk Magazine, December, 82-87 (2013)

[15]

Collin-Dufresne, P, Goldstein, R, Hugonnier, J:A general formula for valuing defaultable securities.Econometrica. 72(5), 1377-1407 (2004)

[16]

Crépey, S:Bilateral counterparty risk under funding constraints. Part I:Pricing, followed by Part II:CVA. Math. Finance. 25(1), 1-50 (2015). First published online on 12 December 2012

[17]

Crépey, S, Élie, R, Sabbagh, W:When capital is a funding source:The XVA Anticipated BSDEs (2017). Working paper available at https://math.maths.univ-evry.fr/crepey

[18]

Crépey, S, Song, S:Counterparty risk and funding:Immersion and beyond. Finance Stochast. 20(4), 901-930 (2016)

[19]

Duffie, D, Huang, M:Swap rates and credit quality. J. Finance. 51, 921-950 (1996)

[20]

Duffie, D, Schroder, M, Skiadas, C:Recursive valuation of defaultable securities and the timing of resolution of uncertainty. Ann. Appl. Probab. 6(4), 1075-1090 (1996)

[21]

Kruse, T, Popier, A:BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration. Stochastics:Int. J. Probab. Stochast. Process. 88(4), 491-539 (2016)

[22]

Piterbarg, V:Funding beyond discounting:collateral agreements and derivatives pricing. Risk Mag. 2, 97-102 (2010)

[23]

Pykhtin, M:Model foundations of the Basel III standardised CVA charge. Risk Magazine (2012)

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