Fast Simulation of Capital Allocation for Credit Portfolios

Project: Research

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The recent financial tsunami has highlighted the needs of more active management of credit portfolios. In many financial institutions, the measurement of portfolio credit risk has been a standard practice. However, risk measurement is only a first step towards active risk management. For purposes such as evaluating the risk of a subportfolio and optimizing the portfolio, one also needs to know how to decompose the total credit risk into a sum of risk contributions for individual transactions or counterparties. These risk contributions can then be used to allocate capital.Typically, value-at-risk is often used as a risk measure for credit portfolios, and it can be decomposed into a sum of risk contributions for individual transactions or counterparties. For most commonly used models, there are no closed-form formulas available for the calculation of risk contributions, and hence one needs to resort to numerical methods, among which Monte Carlo simulation is the most commonly used one. However, simulating risk contributions is computationally challenging. The major challenge is that risk contributions are expectations conditional on rare events, which makes it difficult to estimate them by using crude Monte Carlo estimators.To the best of our knowledge, current methods in the literature on simulating risk contributions mainly focused on the use of importance sampling (IS), a well-known simulation technique, to reduce the variances of the estimators. IS was used to twist the probability measure such that there would be more samples dropping in the domain of the rare event. However, theoretically these methods may not achieve the fastest convergence rates, and empirically it has been documented that their computational results are not yet satisfactory.This project aims to develop efficient methods for simulating risk contributions. The main idea is to use IS in a very different way so that all the samples generated will drop in the domain of the rare event. By doing so, we expect that the proposed method can achieve the fastest convergence rate. Hopefully it will perform better than the available methods in the literature, both theoretically and empirically.Although the method is proposed under the context of capital allocation for credit portfolios, it may also be useful in some other important applications, including fixedincome portfolio selection problem, and the measurement of systemic risk of financial systems. Incorporating the proposed method into these two applications will also be an important part of the project.


Project number9041704
Grant typeGRF
Effective start/end date1/01/1226/09/14