Assistant Professor (Maître de conférences)

Laboratoire de Probabilités, Statistique et Modélisation (LPSM)

Université Paris Cité (Paris Diderot)

Case 7012

75205 Paris Cedex 13

France

Office: Sophie Germain building, nr. 539

Tel:  +33 1 57 27 91 87

E-mail: grbac[at]math.univ-paris-diderot[dot]fr

Research

Publications and preprints:

• Term structure modelling with overnight rates beyond stochastic continuity (2023), with C. Fontana and T. Schmidt
  Forthcoming in Mathematical Finance [arXiv]

• Consistency of traded option prices and absence of arbitrage in the presence of stochastic interest rates (2020), with B. Acciaio
  Preprint [pdf]

• Long-time trajectorial large deviations for affine stochastic volatility models and application to variance reduction for option pricing (2021),
  with D. Krief and P. Tankov
  Advances in Applied Probability 53, 220–250. [arXiv]

• Term structure modeling for multiple curves with stochastic discontinuities (2020), with C. Fontana, S. Gümbel and T. Schmidt
  Finance and Stochastics 24, 465–511. [arXiv]

• Multiple curve Lévy forward price model allowing for negative interest rates (2020), with E. Eberlein and Ch. Gerhart
  Mathematical Finance 30(1), 167–195. [arXiv]

• Martingale property of exponential semimartingales: A note on explicit conditions and applications to financial models (2017), with D. Criens and K. Glau
  Applied Mathematical Finance 24(1) 23–37. [arXiv]

• Approximate option pricing in the Lévy Libor model (2016), with D. Krief and P. Tankov
  In J. Kallsen, A. Papapantoleon (Eds.), Advanced Modelling in Mathematical Finance - In honour of Ernst Eberlein , Springer, 453–476. [arXiv]

• A unified view of LIBOR models (2016), with K. Glau and A. Papapantoleon
  In J. Kallsen, A. Papapantoleon (Eds.), Advanced Modelling in Mathematical Finance - In honour of Ernst Eberlein , Springer, 423–452. [arXiv]

• Derivative pricing for a multicurve extension of the Gaussian, exponentially quadratic short rate model (2016), with L. Meneghello and W. J. Runggaldier
  In Glau, K., Grbac, Z., Scherer, M., Zagst, R. (Eds.), Innovations in Derivatives Markets - Fixed Income Modeling, Valuation Adjustments, Risk Management, and Regulation, Springer, 191–226. [arXiv]

• Affine LIBOR models with multiple curves: theory, examples and calibration (2015), with A. Papapantoleon, J. Schoenmakers and D. Skovmand
  SIAM Journal on Financial Mathematics 6(1), 984–1025. [arXiv]

• A Lévy HJM multiple-curve model with application to CVA computation (2015), with S. Crépey, N. Ngor and D. Skovmand
  Quantitative Finance 15(3), 401–419. [SSRN]

• Information, no-arbitrage and completeness for asset price models with a change point (2014), with C. Fontana, M. Jeanblanc and Q. Li
  Stochastic Processes and their Applications 124(9), 3009–3030. [arXiv]

• Discrete tenor models for credit risky portfolios driven by time-inhomogeneous Lévy processes (2013), with E. Eberlein and T. Schmidt
  SIAM Journal on Financial Mathematics 4(1), 616–649. [arXiv]

• Counterparty risk and funding: The four wings of the TVA (2013), with S. Crépey, R. Gerboud and N. Ngor
  International Journal of Theoretical and Applied Finance 16(2), 1350006. [arXiv]

• Pricing and calibration in market models (2012), with F. Gehmlich and T. Schmidt
  Credit Securitisations and Derivatives - Challenges for the Global Markets, D. Rösch and H. Scheule (Eds.), Wiley, 245–270.

• A tractable LIBOR model with default risk (2013), with A. Papapantoleon
  Mathematics and Financial Economics 7(2), 203–227. [arXiv]

• A multiple-curve HJM model of interbank risk (2012), with S. Crépey and H.-N. Nguyen
  Mathematics and Financial Economics 6(3), 155–190. [pdf]

• Rating based Lévy Libor model (2013), with E. Eberlein
  Mathematical Finance 23(4), 591–626. [SSRN]

Books

• Z. Grbac and W. J. Runggaldier (2016). Interest Rate Modeling: Post-Crisis Challenges and Approaches.
  SpringerBriefs in Quantitative Finance, Springer.

• Glau, K., Grbac, Z., Scherer, M., Zagst, R. (Eds.) (2016). Innovations in Derivatives Markets - Fixed Income Modeling, Valuation Adjustments, Risk Management, and Regulation. Springer.

Doctoral thesis

• Z. Grbac (2010). Credit Risk in Lévy Libor Modeling: Rating Based Approach.
  Ph.D. Thesis, University of Freiburg. Directed by Ernst Eberlein. [pdf]

Teaching

Co-director of the Master program M2 Isifar at Université Paris Cité

Current teaching (2023/2024):

     Modèles avancés de la courbe des taux (cours, Master M2MO)

Modèles de taux (cours, Master M2 Isifar)

Mathématiques de l'assurance (cours, Master M2 Isifar)

Encadrement des projets théoriques en mathématiques financières (Master M1 Isifar)

Teaching 2022/2023:

Modèles avancés de la courbe des taux (cours, Master M2MO)

Modèles de taux (cours, Master M2 Isifar)

Mathématiques financières (TD, Master M1 MFA)

Encadrement des projets théoriques en mathématiques financières (Master M1 Isifar)

Bachelier course: Recent developments in interest rate modeling (2022, Institut Henri Poincaré, Paris)