Modern risk systems
Papers published in 2008

Companion sites: Russian version


  1. A.Novosyolov, D.Satchkov Global term structure modelling using principal component analysis. Journal of Asset Management (2008) 9, 1, 49-60.
    Abstract.
    Principal component analysis (PCA) is a technique commonly applied to the interest rate markets to describe yield curve dynamics in a parsimonious manner. Despite an increase in global investing and the growing interconnectedness of the international markets, PCA has not been widely applied to decomposing joint structure of global yield curves. Our objective is to describe the joint structure with a model that can potentially be used for scenario analysis and for estimating the risk of interest rate-sensitive portfolios. In this study, we examine three variations of the PCA technique to decompose global yield curve and interest rate implied volatility structure. We conclude that global yield curve structure can be described with 1520 factors, whereas implied volatility structure requires at least 20 global factors. The procedure that we identify as preferable is a two-step PCA, with local curves decomposed in the first step and combined local PCs decomposed into a joint structure (PCA of PCs) in the second step. This procedure has a key advantage in that it makes any scenario analysis more meaningful by keeping local PCA factors, which have important economic interpretations as shift, twist and butterfly moves of the yield curve.
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  2. A.Novosyolov Measuring Risk. Reliability and Risk Analysis: Theory and Applications (2008) 1, 4, 115-119.
    Abstract.
    Problem of representation of human preferences among uncertain outcomes by functionals (risk measures) is being considered in the paper. Some known risk measures are presented: expected utility, distorted probability and value-at-risk. Properties of the measures are stated and interrelations between them are established. A number of methods for obtaining new risk measures from known ones are also proposed: calculating mixtures and extremal values over given families of risk measures.
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  3. Novosyolov A.A. Generators of distorted probability functionals. Proceedings of the 8th International Scientific School "Modelling and Analysis of Safety and Risk in Complex Systems", St.-Petersburg, 2008, 290-294.
    Abstract
    The concept of coherent risk measure is defined axiomatically, and every such measure may be represented by a cone of admissible risks or a family of probability distributions. Similar representations are valid for a partial case of coherent risk measures, the so called distorted probability functionals. In the present paper we discuss the specific representation of distorted probability functionals by families of probability measures, and use it to clarify the specific position of distorted probability functionals among coherent risk measures.
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  4. Novosyolov A.A. Higher order stochastic dominance in option pricing and insurance. Proceedings of the 8th International Scientific School "Modelling and Analysis of Safety and Risk in Complex Systems", St.-Petersburg, 2008, 77-82.
    Abstract
    The paper contains derivation of integral and asymptotic representations for complementary distribution functions. A few examples illustrate direct and dual second order stochastic dominance in terms of insurance and option pricing.
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  5. Novosyolov A.A. Some properties of a relative mean functional. Proceedings of the VII All-Russian FAM conference, v. 1, Krasnoyarsk, 2008. (translated from Russian)
    Abstract
    Description of preferences over a set of risks is usually provided by a functional on a set of risks, or by a partial ordering of the set of risks. Stochastic dominance may serve an example for cumulative distribution functions representing risks. Another risk describer, the Omega function, was introduced in \cite{CasconKeatingShadwick2003} for risks with finite expectation. The function equals to ratio of two integrals related with mean, so it is called relative mean function here. The paper is devoted to studying properties of the relative mean function, its relation to stochastic dominance, statistical estimation from observations, and examples of applications to decision-making. Unavailable for downloading.


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