Computation of VaR for portfolios in intensity models

ABSTRACT

In this article, we calculate the value-at-risk (VaR) for large portfolios in intensity models, where the idiosyncratic and systematic risk exposures as well as the impact of past default losses are subsumed into the intensity processes. The adopted method is based on the theory of saddlepoint approximation for continuous-time Markov processes whose transition densities and distribution functions can be approximated in closed forms. A simple example with theoretical and numerical results is presented in the end.

KEYWORDS:

• Value-at-risk
• intensity processes
• saddlepoint approximation

Notes

1 We thank an anonymous referee for suggesting this model.

2 We do not provide the lengthy expression for ${\mathcal{A}}^3{e}^{ul}/e^{ul}$ here to save space; however, we will show it for the concrete example in the next subsection.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (No. 11801407 and 72171164).