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Arbitragefree pricing of derivatives in nonlinear market models
Continuous tenor extension of affine LIBOR models with multiple curves and applications to XVA
1. Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece; 
2. Institut fur Mathematische Stochastik, TU Dresden, 01062 Dresden, Germany 
References:
[1] 
Beveridge, C, Joshi, M:Interpolation schemes in the displaceddiffusion LIBOR market model. SIAM. J. Finan. Math. 3, 593604 (2012) 
[2] 
Bichuch, M, Capponi, A, Sturm, S:Arbitragefree XVA. Math.Finan. (2016). https://arxiv.org/abs/1608.02690 
[3] 
Björk, T:Arbitrage Theory in Continuous Time, 3rd edition. Oxford University Press, Chichester (2009) 
[4] 
Brigo, D, Morini, M, Pallavicini, A:Counterparty Credit Risk, Collateral and Funding:with Pricing Cases for all Asset Classes. Wiley (2013) 
[5] 
Crépey, S:Bilateral Counterparty risk under funding constraintsPart I:Pricing. Math. Finan. 25, 122(2015a) 
[6] 
Crépey, S:Bilateral Counterparty risk under funding constraintsPart II:CVA. Math. Finan. 25, 2350(2015b) 
[7] 
Crépey, S, Bielecki, TR:Counterparty Risk and Funding:A Tale of two Puzzles. Chapman & Hall/CRC Financial Mathematics Series. CRC Press, Boca Raton (2014). With an introductory dialogue by Damiano Brigo 
[8] 
Crépey, S, Grbac, Z, Nguyen, HN:A multiplecurve HJM model of interbank risk. Math. Financ. Econ. 6, 155190 (2012) 
[9] 
Crépey, S, Gerboud, R, Grbac, Z, Ngor, N:Counterparty risk and funding:The four wings of the TVA. Int. J. Theor. Appl. Financ. 16(1350006) (2013) 
[10] 
Crépey, S, Grbac, Z, Ngor, N, Skovmand, D:A Lévy HJM multiplecurve model with application to CVA computation. Quant. Financ. 15, 401419 (2015) 
[11] 
Cuchiero, C, Fontana, C, Gnoatto, A:Affine multiple yield curve models. Preprint. arXiv:1603.00527(2016) 
[12] 
Duffie, D, Filipovic, D, Schachermayer, W:Affine processes and applications in finance. Ann. Appl. Probab. 13, 9841053 (2003) 
[13] 
Filipović, D:Timeinhomogeneous affine processes. Stoch. Process. Appl. 115, 639659 (2005) 
[14] 
Glau, K, Grbac, Z, Papapantoleon, A:A unified view of LIBOR models. In:Kallsen, J, Papapantoleon, A (eds.) Advanced Modelling in Mathematical FinanceIn Honour of Ernst Eberlein, pp. 423452. Springer, Cham (2016) 
[15] 
Grbac, Z, Runggaldier, WJ:Interest Rate Modeling:PostCrisis Challenges and Approaches. Springer, Cham (2015) 
[16] 
Grbac, Z, Papapantoleon, A, Schoenmakers, J, Skovmand, D:Affine LIBOR models with multiple curves:theory, examples and calibration. SIAM. J. Financ. Math. 6, 9841025 (2015) 
[17] 
Jacod, J, Shiryaev, AN:Limit Theorems for Stochastic Processes, 2nd edition. Springer, Berlin Heidelberg (2003) 
[18] 
KellerRessel, M:Affine Processes:Theory and Applications to Finance. PhD thesis, TU Vienna (2008) 
[19] 
KellerRessel, M:Affine LIBOR models with continuous tenor (2009). Unpublished manuscript KellerRessel, M, Papapantoleon, A, Teichmann, J:The affine LIBOR models. Math. Financ. 23, 627658(2013) 
[20] 
Mercurio, F:Interest rates and the credit crunch:New formulas and market models. Preprint. SSRN/1332205 (2009) 
[21] 
Mercurio, F:A LIBOR market model with a stochastic basis. Risk. 8489 (2010) 
[22] 
Musiela, M, Rutkowski, M:Continuoustime term structure models:forward measure approach. Financ. Stoch. 1, 261291 (1997) 
[23] 
Musiela, M, Rutkowski, M::Martingale Methods in Financial Modelling, 2nd edition. Springer, Berlin Heidelberg (2005) 
[24] 
Papapantoleon, A:Old and new approaches to LIBOR modeling. Stat. Neerlandica. 64, 257275 (2010) 
show all references
References:
[1] 
Beveridge, C, Joshi, M:Interpolation schemes in the displaceddiffusion LIBOR market model. SIAM. J. Finan. Math. 3, 593604 (2012) 
[2] 
Bichuch, M, Capponi, A, Sturm, S:Arbitragefree XVA. Math.Finan. (2016). https://arxiv.org/abs/1608.02690 
[3] 
Björk, T:Arbitrage Theory in Continuous Time, 3rd edition. Oxford University Press, Chichester (2009) 
[4] 
Brigo, D, Morini, M, Pallavicini, A:Counterparty Credit Risk, Collateral and Funding:with Pricing Cases for all Asset Classes. Wiley (2013) 
[5] 
Crépey, S:Bilateral Counterparty risk under funding constraintsPart I:Pricing. Math. Finan. 25, 122(2015a) 
[6] 
Crépey, S:Bilateral Counterparty risk under funding constraintsPart II:CVA. Math. Finan. 25, 2350(2015b) 
[7] 
Crépey, S, Bielecki, TR:Counterparty Risk and Funding:A Tale of two Puzzles. Chapman & Hall/CRC Financial Mathematics Series. CRC Press, Boca Raton (2014). With an introductory dialogue by Damiano Brigo 
[8] 
Crépey, S, Grbac, Z, Nguyen, HN:A multiplecurve HJM model of interbank risk. Math. Financ. Econ. 6, 155190 (2012) 
[9] 
Crépey, S, Gerboud, R, Grbac, Z, Ngor, N:Counterparty risk and funding:The four wings of the TVA. Int. J. Theor. Appl. Financ. 16(1350006) (2013) 
[10] 
Crépey, S, Grbac, Z, Ngor, N, Skovmand, D:A Lévy HJM multiplecurve model with application to CVA computation. Quant. Financ. 15, 401419 (2015) 
[11] 
Cuchiero, C, Fontana, C, Gnoatto, A:Affine multiple yield curve models. Preprint. arXiv:1603.00527(2016) 
[12] 
Duffie, D, Filipovic, D, Schachermayer, W:Affine processes and applications in finance. Ann. Appl. Probab. 13, 9841053 (2003) 
[13] 
Filipović, D:Timeinhomogeneous affine processes. Stoch. Process. Appl. 115, 639659 (2005) 
[14] 
Glau, K, Grbac, Z, Papapantoleon, A:A unified view of LIBOR models. In:Kallsen, J, Papapantoleon, A (eds.) Advanced Modelling in Mathematical FinanceIn Honour of Ernst Eberlein, pp. 423452. Springer, Cham (2016) 
[15] 
Grbac, Z, Runggaldier, WJ:Interest Rate Modeling:PostCrisis Challenges and Approaches. Springer, Cham (2015) 
[16] 
Grbac, Z, Papapantoleon, A, Schoenmakers, J, Skovmand, D:Affine LIBOR models with multiple curves:theory, examples and calibration. SIAM. J. Financ. Math. 6, 9841025 (2015) 
[17] 
Jacod, J, Shiryaev, AN:Limit Theorems for Stochastic Processes, 2nd edition. Springer, Berlin Heidelberg (2003) 
[18] 
KellerRessel, M:Affine Processes:Theory and Applications to Finance. PhD thesis, TU Vienna (2008) 
[19] 
KellerRessel, M:Affine LIBOR models with continuous tenor (2009). Unpublished manuscript KellerRessel, M, Papapantoleon, A, Teichmann, J:The affine LIBOR models. Math. Financ. 23, 627658(2013) 
[20] 
Mercurio, F:Interest rates and the credit crunch:New formulas and market models. Preprint. SSRN/1332205 (2009) 
[21] 
Mercurio, F:A LIBOR market model with a stochastic basis. Risk. 8489 (2010) 
[22] 
Musiela, M, Rutkowski, M:Continuoustime term structure models:forward measure approach. Financ. Stoch. 1, 261291 (1997) 
[23] 
Musiela, M, Rutkowski, M::Martingale Methods in Financial Modelling, 2nd edition. Springer, Berlin Heidelberg (2005) 
[24] 
Papapantoleon, A:Old and new approaches to LIBOR modeling. Stat. Neerlandica. 64, 257275 (2010) 
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