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Corporate security prices in structural credit risk models with incomplete information
Author(s) -
Frey Rüdiger,
Rösler Lars,
Lu Dan
Publication year - 2019
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12176
Subject(s) - asset (computer security) , derivative (finance) , econometrics , credit risk , stochastic differential equation , computer science , economics , actuarial science , financial economics , mathematics , computer security
Abstract The paper studies derivative asset analysis in structural credit risk models where the asset value of the firm is not fully observable. It is shown that in order to determine the price dynamics of traded securities, one needs to solve a stochastic filtering problem for the asset value. We transform this problem to a filtering problem for a stopped diffusion process and apply results from the filtering literature to this problem. In this way, we obtain an stochastic partial differential equation characterization for the filter density. Moreover, we characterize the default intensity under incomplete information and determine the price dynamics of traded securities. Armed with these results, we study derivative assets in our setup: We explain how the model can be applied to the pricing of options on traded assets and we discuss dynamic hedging and model calibration. The paper closes with a small simulation study.