We consider the class of risk measures associated with optimized certainty equivalents. This class includes several popular examples, such as CV@R and monotone mean-variance. Numerical schemes are developed for the computation of these risk measures using Fourier transform methods. This leads, in particular, to a very competitive method for the calculation of CV@R which is comparable in computational time to the calculation of V@R. We also develop methods for the efficient computation of risk contributions.

A Fourier Approach to the Computation of CV@R and Optimized Certainty Equivalents

We consider the class of risk measures associated with optimized certainty equivalents. This class includes several popular examples, such as conditional value-at-risk (CVaR) and monotone mean–variance. Numerical schemes are developed for the computation of these risk measures using Fourier transform methods. This leads, in particular, to a very competitive method for the calculation of CVaR, which is comparable in computational time to the calculation of VaR. We also develop methods for the efficient computation of risk contributions.

A Fourier approach to the computation of conditional value-at-risk and optimized certainty equivalents

This article presents a semi-Markov process based approach to optimally select a portfolio consisting of credit risky bonds. The criteria to optimize the credit portfolio is based on l∞-norm risk measure and the proposed optimization model is formulated as a linear programming problem. The input parameters to the optimization model are rate of returns of bonds which are obtained using credit ratings assuming that credit ratings of bonds follow a semi-Markov process. Modeling credit ratings by semi-Markov processes has several advantages over Markov chain models, i.e., it addresses the ageing effect present in the credit rating dynamics. The transition probability matrices generated by semi-Markov process and initial credit ratings are used to generate rate of returns of bonds. The empirical performance of the proposed model is analyzed using the real data. Further, comparison of the proposed approach with the Markov chain approach is performed by obtaining the efficient frontiers for the two models.

https://www.econstor.eu/bitstream/10419/237209/1/1729095542.pdf

Portfolio optimization of credit risky bonds: a semi-Markov process approach

Measuring marginal risk contributions in credit portfolios

The aim of this work is to explore how importance sampling (IS) techniques may improve internal banking portfolio optimization models. The current economic downturn contributes to an increase in the credit risk amount of the loan portfolios reducing the quality of the banking credit. In such a difficult economic context, characterized by the credit crunch phenomenon, robust and stable methodologies of credit portfolio risk minimization, based on ‘enhanced’ Monte Carlo simulation (MCS) portfolio models, may encourage Italian banks to finance the real economy by lending also during risky and uncertain economic conditions. For these reasons, our investigation focuses on Italian banking books composed of credit loans to the 23 Italian non-financial economic sectors. In order to reduce the high volatilities both of the estimates of the credit portfolio's tail risk and of the optimal solutions in terms of credit asset allocations, we combine a two-step IS technique with a MCS model in a context of credit portfolio's Conditional Value at Risk minimization. The performance of this improved credit portfolio optimization model, in terms of accuracy of the estimates, has been investigated for the sample Italian loan portfolio in two different phases of the economic cycle, precisely before and during the current financial and economic crisis.

https://papers.ssrn.com/sol3/Delivery.cfm/ECNO_ECNO12019.pdf?abstractid=2449079&mirid=2

Improving Loan Portfolio Optimization by Importance Sampling Techniques: Evidence on Italian Banking Books

In the framework of a standard structural credit portfolio model, we investigate the Monte Carlo based estimation of capital allocation according to expected shortfall. We develop and analyze several variance reduction techniques based on importance sampling, analytic approximations of portfolio loss distributions and a semi-analytical allocation technique. The focus of the paper is on the application of these techniques to large credit portfolios used in economic capital calculations. Our results show that the inherent numerical problems of expected shortfall allocation can be overcome and, as a consequence, economic capital allocation according to expected shortfall is a viable option for financial institutions.

/pdf/efficient-calculation-of-expected-shortfall-contributions-in-3a787o79je.pdf

Efficient calculation of expected shortfall contributions in large credit portfolios

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Efficient calculation of expected shortfall contributions in large credit portfolios