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J. Risk Financial Manag., Volume 7, Issue 4 (December 2014) – 2 articles , Pages 130-164

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Article
Exact Fit of Simple Finite Mixture Models
by Dirk Tasche
J. Risk Financial Manag. 2014, 7(4), 150-164; https://doi.org/10.3390/jrfm7040150 - 20 Nov 2014
Cited by 7 | Viewed by 4449
Abstract
How to forecast next year’s portfolio-wide credit default rate based on last year’s default observations and the current score distribution? A classical approach to this problem consists of fitting a mixture of the conditional score distributions observed last year to the current score [...] Read more.
How to forecast next year’s portfolio-wide credit default rate based on last year’s default observations and the current score distribution? A classical approach to this problem consists of fitting a mixture of the conditional score distributions observed last year to the current score distribution. This is a special (simple) case of a finite mixture model where the mixture components are fixed and only the weights of the components are estimated. The optimum weights provide a forecast of next year’s portfolio-wide default rate. We point out that the maximum-likelihood (ML) approach to fitting the mixture distribution not only gives an optimum but even an exact fit if we allow the mixture components to vary but keep their density ratio fixed. From this observation we can conclude that the standard default rate forecast based on last year’s conditional default rates will always be located between last year’s portfolio-wide default rate and the ML forecast for next year. As an application example, cost quantification is then discussed. We also discuss how the mixture model based estimation methods can be used to forecast total loss. This involves the reinterpretation of an individual classification problem as a collective quantification problem. Full article
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Article
Risk Management of Interest Rate Derivative Portfolios: A Stochastic Control Approach
by Konstantinos Kiriakopoulos and Alexandros Koulis
J. Risk Financial Manag. 2014, 7(4), 130-149; https://doi.org/10.3390/jrfm7040130 - 27 Oct 2014
Viewed by 4736
Abstract
In this paper we formulate the Risk Management Control problem in the interest rate area as a constrained stochastic portfolio optimization problem. The utility that we use can be any continuous function and based on the viscosity theory, the unique solution of the [...] Read more.
In this paper we formulate the Risk Management Control problem in the interest rate area as a constrained stochastic portfolio optimization problem. The utility that we use can be any continuous function and based on the viscosity theory, the unique solution of the problem is guaranteed. The numerical approximation scheme is presented and applied using a single factor interest rate model. It is shown how the whole methodology works in practice, with the implementation of the algorithm for a specific interest rate portfolio. The recent financial crisis showed that risk management of derivatives portfolios especially in the interest rate market is crucial for the stability of the financial system. Modern Value at Risk (VAR) and Conditional Value at Risk (CVAR) techniques, although very useful and easy to understand, fail to grasp the need for on-line controlling and monitoring of derivatives portfolio. The portfolios should be designed in a way that risk and return be quantified and controlled in every possible state of the world. We hope that this methodology contributes towards this direction. Full article
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