This paper presents a new Expected Shortfall (ES) model based on the Quantum Harmonic Oscillator (QHO). It is used to estimate market risk in banks and other financial institutions according to Basel III standard. Predictions of the model agree with the empirical data which displays deviations...

This paper considers risks of the investment portfolio, which consist of distributed mortgages and sold European call options. It is assumed that the stream of the credit payments could fall by a jump. The time of the jump is modeled by the exponential distribution. We suggest that the returns...

Using a limiting approach to portfolio credit risk, we obtain analyticexpressions for the tail behavior of the distribution of credit losses. We showthat in many cases of practical interest the distribution of these losses haspolynomial ('fat') rather than exponential ('thin') tails. Our...