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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2019
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/1906.05898 |
| Etiquetas: |
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- We consider a structural stochastic volatility model for the loss from a large portfolio of credit risky assets. Both the asset value and the volatility processes are correlated through systemic Brownian motions, with default determined by the asset value reaching a lower boundary. We prove that if our volatility models are picked from a class of mean-reverting diffusions, the system converges as the portfolio becomes large and, when the vol-of-vol function satisfies certain regularity and boundedness conditions, the limit of the empirical measure process has a density given in terms of a solution to a stochastic initial-boundary value problem on a half-space. The problem is defined in a special weighted Sobolev space. Regularity results are established for solutions to this problem, and then we show that there exists a unique solution. In contrast to the CIR volatility setting covered by the existing literature, our results hold even when the systemic Brownian motions are taken to be correlated.