Filtering techniques in the modeling, pricing and hedging of interest rate and credit risk

• Applicants: Professor Dr. Rüdiger Frey; Professor Dr. Thorsten Schmidt
• Subject Area: Mathematics
• Term: from 2011 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 196379142

• Final Report Year: 2015

Final Report Abstract

The project was concerned with the analysis of dynamic credit risk models in a setup where key state variables of the model are unobservable, using stochastic filtering techniques. Within this context we studied structural credit risk models with incomplete information, the impact of contagion on counterparty risk and collateralization and certain numerical issues. We obtained a couple of interesting results that open promising avenues for future research. In particular, we plan to work on the statistical analysis of credit risk models under incomplete information, on pricing and hedging of hybrid securities in structural models and on the extension of the methods to sovereign debt risk.

Publications

• (2013) “On Galerkin Approximations for the Zakai Equation with Diffusive and Point Process Observations”, SIAM Journal of Numerical Analysis 51, pp 2036–2062
  Frey, R. and Schmid, T. and Xu, L.
  (See online at https://doi.org/10.1137/110837395)
• (2014) “Contagion effects and collateralized credit value adjustments for credit default swaps”, International Journal of Theoretical and Applied Finance, 17 (7): 1450044/1–29
  Frey, R. and Rösler, L.
  (See online at https://doi.org/10.1142/S0219024914500447)
• “Corporate security prices in structural credit risk models with incomplete information”, Mathematical Finance
  Frey, R., Rösler, L. and Lu, D.
  (See online at https://doi.org/10.1111/mafi.12176)