Current Trends in Financial Modelling

Modelling Dependent Credit Risks

Abstract: In this talk we give an overview of the statistical approaches to modelling dependence that underlie the most important industry credit risk models, including RiskMetrics, CreditRisk+, KMV and CreditPortfolioView. Assumptions concerning the nature of dependence between defaults and credit downgrades crucially affect the tail of the portfolio loss distribution and thus the determination of a credit risk VaR.
   In the existing models two general approaches to modelling dependence may be identified: latent variable models and mixture models. In latent variable models default (or downgrade) occurs if a latent variable, usually interpreted as company asset value, falls below a threshold, usually interpreted as liabilities. In the major industry models the latent variables for a portfolio of obligors are invariably taken to be multivariate normal. To understand the nature of dependence in such models, as well as possible deficiencies of the approach, we introduce the important concepts of copulas and tail dependence.
   The presentation of Dr. Uwe Schmock follows on directly from this talk and deals in greater depth with the mixture modelling approach.

Modelling Dependent Credit Risks

Abstract: In this talk we apply Polya's urn scheme, the theory of exchangeable sequences and martingale convergence to justify the Dirichlet-binomial distribution for modelling the number of defaults in a credit portfolio. The portfolio consists of homogeneous groups characterized by their credit ratings. The random default probabilities for members of the different groups preserve the strict monotonicity according to the credit rating; this induces a hierarchical dependence structure. A special feature of the model is the fact that it can be fitted easily to Standard & Poors's data, for example. Iterated urn schemes and extensions to random credit rating transition matrices are discussed.

Coherent Risk Measures in Multiperiod Models

Decentralized Risk Management Using Coherent Measures of Risk

Abstract: We begin with a review of coherent risk measures for regulation of risk. We then consider a more general class of risk measures suitable for managing risk to satisfy a shareholder, and discuss the relationship of these measures to utility theory. We then apply these risk measures to the problem of firm-wide risk management; specifically we introduce a structure for allowing desks in a firm to trade risk limits in an internal market among themselves. Assuming that desks seek to maximize expected return subject to constraints imposed by these risk limits, we show that the internal market for changes in risk limits has an equilibrium which produces optimal firm behavior.

Real Option Valuation in Investment Planning Models

Abstract: The financial community has used option valuation models for many years to price contingent claims or derivatives of underlying financial assets. Many firms have now also used these general ideas to value real options, investment decisions involving real assets. In this context, the investment may represent the exercise of an option to build or purchase capacity, develop a product, or license intellectual property. After exercising the option, cash flows result as in the financial context, allowing the application of similar valuation techniques.
   This talk will describe the valuation of real options and their use for practical investment decisions. The presentation will also highlight advantages of real option approaches over traditional net present value analyses, in particular for investments where delay or adding flexibility may increase value. Discussion will include how optimization models can incorporate real options into an overall strategic investment framework, what differences exist between financial options and real options, and what key factors to include in using real option models in practice.

Scenario Optimisation Asset and Liability Modelling for Endowments with Minimum Guarantees

Abstract: Endowments with a minimum guaranteed rate of return appear in insurance policies, pension plans and social security plans. In several cases, especially in the insurance industry, such endowments also participate in the business and receive bonuses from the firm's asset portfolio. In this talk we develop a scenario based optimization model for asset and liability management of participating insurance policies with minimum guarantees. The model allows the analysis of the tradeoffs facing an insurance firm in structuring its policies as well as the choices in covering their cost. The model is applied to the analysis of policies offered by Italian insurance firms. While the optimized model results are in general agreement with current industry practices, inefficiencies are still identified and potential improvements are suggested.
   The modeling tools developed for the management of insurance policies are also used to develop a web-based system for individual investors. Investor's goals and risk profiles are addressed in an integrated fashion. The requirements for real-time modeling by the average investor must be reflected in the model, and this issue will be discussed as well. The practical experience with this model will be discussed.

References:

• A. Consiglio, F. Cocco and S.A. Zenios, Scenario optimization asset and liability modeling for endowments with guarantees, Working paper 00-41, The Wharton Financial Institutions Center, The Wharton School, University of Pennsylvania, PA, 2000.
• A. Consiglio, F. Cocco and S.A. Zenios, The value of integrative risk management for insurance products with guarantees, Journal of Risk Finance, pp. 1-11, Spring 2001.
• S.A. Zenios et. al. , Dynamic models for fixed-income portfolio management under uncertainty, Journal of Economic Dynamics and Control, 22: 1517-1541, 1998.

Financial Applications of Stochastic Programming

Abstract: Stochastic programming is a methodology for financial decision making that overcomes many limitations of traditional approaches. Uncertainty in risk factors like interest and exchange rates, prices, or cash flows is taken into account by generating representative scenarios for their possible future outcomes. A stochastic program is particuarly useful when constraints must be incorporated. Moreover, possible correlations between interest rates and volumes as they are observed for saving deposits and non-fixed rate mortgages can be exploited more appropriately than in static methods like the replicating portfolio approach.
   In our contribution we introduce a model for managing non-maturing account positions taking into account the bid/ask spread with increasing transaction limits due to liquidity restrictions as well as restrictions on the duration and portfolio composition. In addition, a short introduction to the barycentric approximation is provided, which is used for discretizing the underlying stochastic dynamics. We conclude with the presentation of several case studies and their numerical results.

An Asset-Liability Management System for an Insurance Company

Abstract: Modern property casualty insurance companies face a convergence of risks across assets and liabilities. An integrated financial planning system assists company executives with significant decisions, such as asset allocation and mergers/acquisitions, while monitoring and controlling company-wide risks. Numerous examples of ALM systems have been implemented, including Tillinghast-Towers Perrin,Renaissance Re-Insurance, and American Re-Insurance. The pro/cons of the alternative modeling approaches will be discussed, especially comparing multi-stage stochastic programs and policy optimization. A real-world ALM system will illustrate the issues.