Talks in Financial and Insurance Mathematics, Winter 2002/03

• Daniel Straumann (Laboratory of Actuarial Mathematics, University of Copenhagen)
  Quasi-maximum-likelihood estimation in heteroscedastic time series: a stochastic recurrence equations approach
  
  Abstract: We study the quasi-maximum-likelihood estimator (QMLE) in a general heteroscedastic time series model of multiplicative form
  
  
  X_t = s_tZ_t,      s_t² = g_i(X_t-1,s_t-1²),      t in Z,
  
  where {g_i} denotes a parametric family of non-negative functions on R x [0,infinity) fulfilling certain conditions and (Z_t) is a sequence of centered i.i.d. random variables with variance 1. Using the techniques of stochastic recurrence equations, the existence and uniqueness of a stationary solution (X_t) is shown, and consistency and asymptotic normality of the QMLE are established. The resulting theory is applied to popular financial time series models: GARCH(1,1), asymmetric GARCH(1,1) and EGARCH.

• Awarding of the Walter Saxer Insurance Prize
  
  

  Winner	Maik André Berchtold (D-MATH, ETHZ) for his diploma thesis Simulation von Diffusionsprozessen aus diskreten Beobachtungen under the supervision of Prof. Dr. H.-R. Künsch.
  Laudatio	Prof. Dr. Peter Bühlmann (Seminar for Statistics, ETH Zürich)
  Talk	Prof. Dr. André Dubey (University of Lausanne, Price winner 1978) Gedanken zur Solvabilität in der Nichtlebenversicherung
  Apero	Main Hall of ETHZ (offered by Generali Versicherungen)

• Dr. Christoph Hummel (Converium)
  Kapitalallokation unter Berücksichtigung von Abhängigkeiten zwischen Großschäden
  
  Abstract: Aus der Sicht eines Rückversicherers wird ein Kapitalallokationskonzept vorgestellt, welches Abhängigkeiten zwischen Großschäden berücksichtigt. Im ersten Teil des Vortrages wird kurz auf die Theorie eingegangen. Danach wird gezeigt, wie dieses Konzept in die Praxis umgesetzt werden kann, um Rückversicherungsverträge zu tarifieren.

• Silvan Ebnöther (University of Southern Switzerland and ZKB)
  Operational risk for networks
  
  Abstract: Operational risk, or the risk of failure and malfunctions of people and systems in financial institutions, has properties that are substantially different from those of market and credit risk. First, the sources of risk entering the definition of "operational risk" are complicated objects with a far richer structure than the two other risk-categories of market and credit risk. Second, between the operational risk factors strong and non-trivial dependencies typically exist, which cannot be captured by the usual "covariance matrix approach". Therefore, we motivate an approach from the sciences of disordered media, and show why this approach is a natural choice for modelling operational risk within IT networks. Setting up such a model for a suitably large network, we analyze the effect of operational risk management activities on loss and risk figures. (Joint work with Markus Leippold and Paolo Vanini.)

• Dr. Pablo Koch-Medina (Swiss Re)
  The economics of insurance
  
  Abstract: One of the fundamental questions any business needs to answer is how they create value for their owners. This is related to the question of determining the production costs for the products that are sold. For financial intermediaries this is a tricky question which boils down to determining the cost of taking insurance risk. In answering this question there has traditionally been a large gap between finance experts and actuaries. Based on standard corporate finance theory, finance oriented professionals claim that diversifiable risks such as insurance risks comes at no extra costs to shareholders, i.e., that the amount by which premiums exceed expected claims and expenses is all true economic profit. In contrast, actuaries have traditionally ignored this and have always attached a loading interpreted as a compensation for taking insurance risks. In this talk we try to build a bridge between these two diverging views by integrating modern results in corporate finance. The presentation draws on the framework described in "The economics of insurance: how insurers create value for shareholders" which can be obtained at the publications download section in www.swissre.com.

• Prof. Dr. Wolfgang Kürsten (Friedrich-Schiller-Universität Jena)
  Risiko, Shareholder Value und Unternehmenswert
  - Das Problem "Synergetische Merger" und andere Beispiele
  
  Abstract: Wertsteigerungskonzepte und Entscheidungen über die Risikopolitik des Unternehmens sind wesentliche Bestandteile von Rappaports Shareholder Value-Prinzip. Die aktuelle Diskussion um dessen Rolle als Instrument kapitalmarktorientierter Unternehmensführung differenziert unzureichend nach den Wegen, wie und für wen Wertsteigerungen erreicht werden sollen. Unzureichend ist es beispielsweise, wenn Wertsteigerungen auf Gesamtunternehmensebene mit Wertsteigerungen bei der Eigenkapitalposition der Aktionäre gleichgesetzt werden, wie man das etwa an der gelegentlichen Euphorie über synergetische Unternehmenszusammenschlüsse ablesen kann. Der Vortrag will hier zu einer theoretischen Fundierung und Systematisierung der Argumente beitragen. Dazu wird das Shareholder Value-Prinzip im Lichte neoklassischer und informations-ökonomischer Bausteine der modernen Finanzierungstheorie konkretisiert und untersucht, welche Risikopolitiken grundsätzlich zu Wertsteigerungen im Aktionärsinteresse führen. Anhand konkreter Beispiele - Flexibilitätsoptionen, Managerentlohnung mit Stock Options, Synergetische Merger - läßt sich zeigen, daß eine (vermeintliche) Vorteilhaftigkeit bestimmter Unternehmensentscheidungen allenfalls im konkreten Modellkontext und nur bei Annahme bestimmter Informationsverteilungen zwischen Shareholdern und Stakeholdern beurteilt werden kann. So liegen beispielsweise synergetische Merger trotz ihrer positiven Gesamtwerteffekte einerseits nicht zwingend im Aktionärsinteresse, können aber andererseits positive moral hazard-induzierte Risikoeffekte für die Shareholder nach sich ziehen. In der Gesamtsicht wird die (häufig polit-ökonomisch geführte) Diskussion über Pro und Contra einer am Shareholder Value orientierten Unternehmenssteuerung ohne finanzierungstheoretische Fundierung der Argumente kaum auskommen, dann aber nur deutlich relativierte Handlungsempfehlungen zulassen.

• Dr. Alexander Stremme (Warwick Business School)
  Asset pricing and conditioning information: factor models and portfolio efficiency
  
  Abstract: In this talk, we construct portfolio-based tests of conditional factor models, developed by exploiting the close link between the stochastic discount factor framework and unconditional mean-variance efficiency. We show that an asset pricing model admits a conditional factor representation if and only if there is some combination of the factor mimicking portfolios that is unconditionally mean-variance efficient. Conversely, for a given set of factors, our analysis allows us to construct a managed portfolio of the factor mimicking portfolios that attains the maximum Sharpe ratio generated by the factors. We thus obtain the factor loadings, as functions of the conditioning information, of the optimal conditional factor model for given choice of factors. We use our results to empirically test several factor models proposed in the literature. We find that the Consumption Capital Asset Pricing Model, scaled by lagged consumption-wealth ratio, as well as the model of Harvey and Siddique (2000) perform comparatively well as conditional asset pricing models, while the Fama and French (1992) model does less well.

• Prof. Dr. Paul Embrechts (D-MATH, ETH Zürich)
  Ruin, operational risk and time change
  
  Abstract: After credit and market risk, and mainly due to the new Basel II proposals, operational risk is an important new source of risk for financial institutions to be concerned about. In this talk I discuss how quantitative modelling of operational risk links up with current (and past) research in insurance risk theory. Papers related to this talk are:
  1. Embrechts, P., Kaufmann, R., Samorodnitsky G. (2002): Ruin theory revisited: stochastic models for operational risk (preprint).
  2. Embrechts, P., Samorodnitsky G. (2001): Ruin problem, operational risk and how fast stochastic processes mix (to appear in Annals of Applied Probability).
  They can be downloaded via my home page, some selected papers.

• Prof. Dr. Denis Talay (INRIA Sophia Antipolis, France)
  Accuracy of the Monte Carlo method for VaR-type approximations for diffusion models

• Prof. Dr. Jeremy Staum (School of Operations Research and Industrial Engineering, Cornell University)
  Pricing and hedging in incomplete markets: Fundamental theorems and robust utility maximization
  
  Abstract: We prove fundamental theorems of asset pricing for good-deal bounds in incomplete markets, relating arbitrage-freedom and uniqueness of prices to existence and uniqueness of a pricing kernel with appropriate properties. The technology employed is duality of convex optimization in locally convex linear topological spaces. The concepts investigated are closely related to convex and coherent risk measures, exact functionals, and coherent lower previsions in the theory of imprecise probabilities. We apply the results to analyze a specific method for constructing good-deal bounds, based on robust expected utility involving a unanimity rather than a maxmin criterion.

• Guy Castagnoli (Winterthur Life & Pension)
  Actuarial issues in accounting

• Dr. Ursula A. Theiler (Risk Training, Bruckmuehl, Germany)
  Risk-return management approach for the bank portfolio
  
  Abstract: In an intensifying competition banks are forced to develop and implement enterprise wide integrated risk-return management systems. Financial risks have to be limited and managed from a bank wide portfolio perspective. Risk management rules must be accomplished at the same time from internal and regulatory points of view. Expected returns need to be maximized subject to these constraints, leading to a generalized portfolio optimization problem under different capital limits.
       We give a survey on a risk-return management approach for the bank portfolio that applies actual techniques of portfolio risk measurement and optimization to the bank portfolio [6]. We formulate an optimization model for the bank portfolio that maximizes the expected returns subject to internal and regulatory loss risk limitations. The internal risk constraint is based on the risk measure of Conditional Value at Risk (CVaR), that has been proved to be appropriate for measuring bank wide loss risk [3, 4]. We extend the optimization problem by regulatory capital constraints that represent the 'Basle Rules' of loss risk limitation [1, 2]. We apply an algorithm by Rockafellar/Uryasev to solve the optimization problem [3].
       From the optimum portfolio we derive return targets and capital limits for each business line and obtain basic information for a risk-return management process [6]. The risk-return ratios are based on the Euler allocation principle that we apply to estimate the risk contributions of the single assets [5]. The impact of the risk-return management optimization is shown by an application example.
  
  References:
  1. Basle committee on Banking Supervision (1988): International convergence of capital measurement and capital standards, Basle, July 1988.
  2. Basle committee on Banking Supervision committee (1996): Amendment to the capital accord to incorporate market risks, Basle, January 1996.
  3. R.T. Rockafellar and S. Uryasev (2000): Optimization of Conditional Value-At-Risk, The Journal of Risk, Vol. 2, No. 4, pp. 21-51.
  4. R.T. Rockafellar and S. Uryasev (2002): Conditional Value-at-Risk for General Loss Distributions, Journal of Banking and Finance, 27/7.
  5. D. Tasche (1999): Risk Contributions and Performance Measurement. Working Paper, Technische Universität München.
  6. U. Theiler (2002): Optimization Approach for the Risk-Return-Management of the Bank Portfolio, Wiesbaden (Dissertation, in German).

• Prof. Dr. Georg Pflug (Department of Statistics and Decision Support Systems, University of Vienna)
  Risk/Return Konzepte zur Mehrperioden Portfolio Optimierung
  
  Abstract: Einperioden Portfolio Optimierungsprobleme führen typischerweise zu Optimierungsaufgaben mit linearer, quadratischer oder konvexer Zielfunktion und linearen Nebenbedingungen. Der effiziente Rand ergibt sich als Lösungsgesamtheit eines parametrischen Problems.
       Im Mehrperiodenfall wird üblicherweise die terminale Größe (terminal wealth) betrachtet und danach wie im Einperiodenfall vorgegeangen. Diese Vorgangsweise erscheint gerechtfertigt, wenn es klare Endtermine der Planung gibt. Für den Fall, daß jedoch sowohl der Return aber auch das Risiko der Zwischenperioden berücksichtigt werden soll, ergibt sich das Problem, das Risiko im Mehrperiodenfall adäquat zu messen.
       Wir präsentieren ein Konzept der Risikomessung für stochastische Prozesse, zeigen Eigenschaften und vergleichen mit anderen Konzepten. Die Submartingaleigenschaft des Risikomaßprozesses wird erläutert. Das vorgestellte Konzept führt ebenfalls – wie im Einperiodenfall – zu linearen, quadratrischen oder konvexen Optimerungsaufgaben mit linearen Nebenbedingungen. Beispiele zur Portfoliooptimierung werden gegeben.

• PD Dr. Wolfgang Breymann (RiskLab, Department of Mathematics, ETH Zürich)
  Dependence structures for multivariate high-frequency data in finance
  
  Abstract: Stylised facts for univariate high-frequency data in finance are well-known. They include scaling behaviour, volatility clustering, heavy tails, and seasonalities. The multivariate problem, however, has scarcely been addressed up to now. In this talk, bivariate series of high-frequency FX spot data for major FX markets are investigated. First, as an indispensable prerequisite for further analysis, the problem of simultaneous deseasonalisation of high-frequency data is addressed. In the following sections we analyse in detail the dependence structure as a function of the time scale. Particular emphasis is put on the tail behaviour, which is investigated by means of copulas. (The talk is based on joint work with Alexandra Dias and Paul Embrechts.)

• Dr. Michel Dacorogna (Converium)
  Extreme moves in foreign exchange rates and risk limit setting
  
  Abstract: Foreign exchange rates can be subject to considerable daily fluctuations (up to 5% within one day). This can, in certain cases, cause serious losses on open overnight positions. Given a maximum tolerable loss for a company, limits have to be set on open overnight positions in foreign currencies. Usually, these limits are determined by using a normal ("Gaussian") model for the daily fluctuations. In our study we illustrate how this common model sometimes quite strongly underestimates the actual extreme risks and, based on methods from the Extreme Value Theory, we propose and justify a more accurate model. We also show how to use these estimations to compute limits that a risk manager can set to open positions to avoid unexpected huge losses.

• Prof. Dr. Yves Smeers (CORE, Université catholique de Louvain, Belgium)
  Market incompleteness in cross border trade of electricity
  
  Abstract: Discussions on cross-border electricity trade in Europe have been going on for now four years in the context of the so-called Florence Regulatory Forum. The lack of agreement (or the very soft agreements) in the Forum suggests that we are heading towards a market that can be described as very incomplete. This talk analyses this situation through stylized equilibrium models of the electricity market. A first part of the talk briefly describes the proposal of coordinated auction developed by the European Association of Transmission Systems Operators for managing congestion due to cross-border trade of electricity. It then shows how this proposal can only lead to an incomplete market even in a deterministic world. The third part of the presentation extends the previous deterministic model into a two-stage stochastic equilibrium model. This model is used to show that the absence of a balancing market introduces further incompleteness in the market. The equilibrium models that form the basis of the discussion are formulated as simple variational inequality problems. These models are used to support the reasoning, not for presenting numerical results (even though they lead themselves to numerical implementations). The discussion covers both the equilibrium models and their interpretation in terms of the institutional proposals of the Florence Regulatory Forum.

• Prof. Dr. Monique Jeanblanc (Université d'Evry Val d'Essonne, France)
  Default risk and the role of information
  
  Abstract: We are interested in the link between information and hazard rate and study some particular cases: incomplete information and correlated volatilities.
  
  The paper Hazard Rate for Credit Risk and Hedging Defaultable Contingent Claims is available in DVI (64 kB) and PDF format (172 kB).

• Prof. Dr. Hans Bühlmann (Department of Mathematics, ETH Zürich)
  Multidimensional actuarial valuation and control of financial risk
  
  Abstract: In an example it is shown how the actuarial valuation of liabilities can be expressed as a portfolio. This portfolio needs then to be compared with the portfolio of assets. If the two portfolios are different the risk must be controlled either by an appropriate option or by an immobilized capital at risk.

• Joachim Schaller (Partner Re)
  Impaired life annuity - die Rente mit Risikoprüfung

• Prof. Dr. Paolo Vanini (Zürcher Kantonalbank and Università della Svizzera Italiana)
  Modeling operational risk
  
  Abstract: The Basel Committee on Banking Supervision ("the Committee") released a consultative document that included a regulatory capital charge for operational risk. Since the release of the document, the complexity of the concept of "operational risk" has led to vigorous and recurring discussions. We show that for a production unit of a bank with well-defined work flows operational risk can be unambigously defined and modeled. The results of this modeling exercise are relevant for the implementation of a risk management framework, and the pertinent risk factors can be identified. We emphasize that only a small share of all work flows make a significant contribution to the resulting VaR. This result is quite robust under stress testing. Since the definition and maintenance of processes is very costly, this last result is of major practical importance. Finally, the approach allows us to distinguish features of quality management and risk management respectively.
  (The paper is available online.)

• Dr. Jörg Kampen (University of Heidelberg, Germany)
  PDE-schemes for the valuation of American put baskets

• Dr. Céline Azizieh (Université Libre de Bruxelles, former visitor of RiskLab)
  Time series modeling with a multifractal model
  
  Abstract: In the classical Black-Scholes model, if we define the (logarithmic) return of some financial asset at time t for the (fixed) time interval h by
  
  r(t,h) := ln S(t) - ln S(t-h)
  where S(t) denotes the price of the asset at time t, then these returns r(.,h) are i.i.d. Gaussian random variables. In practice however, the returns processes of a number of financial assets show different statistical properties. First, the returns distribution presents heavy tails, the tail index being an increasing function of the considered time interval h. A second observation is the long memory of the realized volatility process, which is directly linked with the so called phenomenon of volatility clustering. Another important observed fact is the presence of scaling laws: Define S_q(h) as the average of |r(jh,h)|^q with j running from 1 to N/h, where N denotes the length of the considered time series. Then S_q(h) seems proportional to |h|^f(q) for some concave function f(q), which suggests multifractality. For all those reasons, new models have been proposed, taking into account those observations.
  
  In this work, we are interested in modelisation of financial time series by fractal and even multifractal models. In a first mathematical part, we recall some notions relative to self-similar and multifractal processes. In a second part, we recall the preceding stylized facts (with illustration on some high frequency data from the foreign exchange market), and we introduce the stochastic cascade model proposed by Breymann-Ghashghaie-Talkner (Journal of Theoretical and Applied Finance, 2000). This is a multifractal model based on an analogy with hydrodynamic turbulence and which tries to reproduce the preceding statistical properties observed in the data. We compare the model to the data and we attempt to estimate some parameters.

Page created and supported by Uwe Schmock until September 2003. Last update: September 13, 2003