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Stochastic Filtering and Corporate and Sovereign Credit Risk

Project Staff:

Leader: Rüdiger Frey
Principal Investigators: Kurt Hornik, Stefan Pichler
Scientific Staff: Christian Diem, Rainer Hirk, Laura Vana
Cooperating Partners: Katia Colaneri, Zehra Eksi-Altay
Former Members: Camilla Damian, Riccardo Rastelli, Michaela Szölgyenyi

Description:

Short Description:

The financial crisis and the following sovereign debt crisis showed that the existing theoretical framework for the modelling of credit and sovereign debt risk is not sufficient to provide empirically sound guidelines for financial decision making: some of the existing models are quite satisfactory from a theoretical perspective, but cannot be directly implemented because of the non-observability of the underlying economic variables. Other models such as the popular credit rating or scoring models are easily applicable, but lack a sound methodology for model validation and empirical testing, essentially because the `true' creditworthiness of a firm is not observable. In this project we will address these issues by a systematic use of stochastic filtering techniques. Stochastic filtering is a mathematical discipline that deals with signal detection and parameter estimation in partially observed systems and is thus a natural tool for the analysis of credit risk. We want to study applications of stochastic filtering to three related areas: analysis of sovereign credit spreads; statistical methodology for credit rating systems; pricing and hedging of financial assets in structural models. We will consider the entire mathematical "production-chain", ranging from mathematical model development and the extension of filtering techniques to the implementation and testing of models on real data. A particular emphasis will be put on statistical inference.

>> Detailed Summary

Publications:
  • Kritzer, Peter, Leobacher, Gunther, Szölgyenyi, Michaela, Thonhauser, Stefan. 2019. Approximation methods for piecewise deterministic Markov processes and their costs. Scandinavian Actuarial Journal 4, 308-335, doi.org/10.1080/03461238.2018.1560357

  • Neuenkirch, Andreas, Szölgyenyi Michaela, Szpruch Lukasz. 2018. An adaptive Euler-Maruyama scheme for stochastic differential equations with discontinuous drift and its convergence analysis. SIAM Journal on Numerical Analysis 57 (1), 378-403. doi.org/10.1137/18M1170017

  • Frey, Rüdiger, Hledik, Juraj. 2018. Diversification and Systemic Risk: A Financial Network Perspective. Risks 6(2), 54; doi.org/10.3390/risks6020054

  • Leobacher, Gunther, Szölgyenyi, Michaela. 2018. Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient. Numerische Mathematik 138 (1), 219–239. doi.org/10.1007/s00211-017-0903-9

  • Damian, Camilla, Eksi, Zehra, Frey, Rüdiger. 2017. EM Algorithm for Markov Chains Observed via Gaussian Noise and Point Process Information: Theory and Case Studies. Statistics & Risk Modeling 35 (1-2), 51–72, doi.org/10.1515/strm-2017-0021

  • Frey, Rüdiger, Rösler, Lars, Lu, Dan. 2017. Corporate security prices in structural credit risk models with incomplete information. Mathematical Finance. 2017;00:1–33. arXiv:1701.04780

  • Leobacher, Gunther, Szölgyenyi, Michaela. 2017. Numerical methods for SDEs with drift discontinuous on a set of positive reach. Internationale Mathematische Nachrichten 235, 1-16. arXiv:1708.06188

  • Eichler, Andreas, Leobacher, Gunther, Szölgyenyi, Michaela. 2017. Utility indifference pricing of insurance catastrophe derivatives. European Actuarial Journal 7 (2), 515–534. doi.org/10.1007/s13385-017-0154-2

  • Leobacher, Gunther, Szölgyenyi, Michaela. 2017. A strong order 1/2 method for multidimensional SDEs with discontinuous drift. Annals of Applied Probability 27 (4), 2383-2418. doi.org/10.1214/16-AAP1262

  • Shardin, Anton A., Szölgyenyi, Michaela. 2016. Optimal control of an energy storage facility under a changing economic environment and partial information. International Journal of Theoretical and Applied Finance 19 (4): S. 1-27. doi.org/10.1142/S0219024916500266

  • Szölgyenyi, Michaela. 2016. Dividend maximization in a hidden Markov switching model. Statistics & Risk Modeling 32 (3-4), 143-158. arXiv:1602.04656

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Preprints:
  • Colaneri, Katia, Eksi, Zehra, Frey, Rüdiger, Szölgyenyi, Michaela: Shall I Sell or Shall I Wait? Optimal Liquidation under Partial Information with Price Impact. arXiv:1606.05079

Third Mission:

Young Science Project: www.youngscience.at

Funded by:

WWTF Wiener Wissenschafts-, Forschungs- und Technologiefonds
(Vienna Science and Technology Fund)
www.wwtf.at/projects/research_projects/details/index.php

WWTF project number: MA14-031
Duration:
01.04.2015 - 31.03.2020