Research Projects at RiskLab

Current research projects and proposals include:
Concluded research projects include:

First Passage Time Probability for Levy-Feller Type
Processes with a View Towards Ruin Probability: A Computational
Approach

First passage time distribution for random processes are key quantities in many fields of sciences. For instance, in actuarial mathematics
it is required in order to estimate the ruin probability of an insurance company. In finance, where jump diffusions have experienced renewed interest, such quantities are also critical for pricing some path-dependent options and for Credit Risk modelling. However, closed form solutions to  this problem are not attainable except in few
specific cases. Moreover, dealing with jumps processes is mathematically much more challenging that the pure diffusion case.
The aim of this project is to compute numerically the first passage time distribution over some fixed or moving boundaries for a large class of
Markov processes including Levy-Feller type processes and additive Markov processes. The methodology consists on solving the backward Kolmogorov
equation associated to the process with some appropriate boundaries conditions.
We propose a flexible numerical scheme based on the Wavelet-Galerkin finite element method to solve the corresponding parabolic integro-differential boundary value problem.
RiskLab/SAM researcher: Dr. Pierre Patie
Project proposal: Prof. Dr. Christoph Schwab (SAM, Department of Mathematics,   ETH Zürich), Dr. Pierre Patie
Start of project: April 1, 2005
Last update: March 6, 2005
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Fast Deterministic Computation of Valuations for Assets Driven by Lévy Processes

The fast numerical valuation of assets whose prices are driven by Brownian motion has become standard practice worldwide. In a Black-Scholes setting, this reduces to the numerical solution of a parabolic partial differential equation with various initial/boundary conditions and possibly constraints. When closed form solutions are not available, numerical methods must be employed; methods for handling such numerical problems have been well developed.
General Lévy processes have been advocated in recent years for models in option pricing. They offer more flexibility than Brownian motion and appear superior e.g. for modelling short-term asset returns whose distributions are heavy-tailed. Lévy models lead to parabolic integro-differential equations with nonlocal Dynkin operators which, in general, cannot be solved in closed form.
The objective of this project is to develop computational methods for the fast numerical solution of pricing problems driven by general Lévy processes. The approach is able to handle general processes and types of contracts, thereby allowing to assess the model sensitivity and model risk.
The infinitesimal generator of the process driving the underlying entails due to its jump component large, ill-conditioned and densely populated matrices which must be inverted in each timestep. Wavelet based discretizations allow to "compress" these matrices to sparse and well-conditioned ones.
The resulting algorithm has log-linear complexity comparable to that of the best finite-difference schemes for the usual Black-Scholes type models, and can accomodate local and stochastic volatility models. Currently, we extended this technology to pricing American contracts on Lévy driven assets.
As part of this project we also addressed the pricing problem for options within stochastic volatility models. While for European Vanilla options closed form expressions are available, other types of contracts, as e.g., compound-style options have to be priced numerically. We developed a wavelet based method which allows to handle the resulting degenerate parabolic partial differential equation due to the stochastic volatility in an optimal fashion.
We also plan to assess model risk and perform sensitivity studies, including deterministic evaluation of the model's "greeks" and model parameter fitting to given market data.
RiskLab/SAM researcher: Dr. Ana-Maria Matache (50% RiskLab, 50% SAM)
Project proposal: Prof. Dr. Christoph Schwab (SAM, Department of Mathematics,ETH Zürich)
Start of project: July 1, 2001
Papers: Fast Deterministic Pricing of Options on Lévy Driven Assets
Wavelet Galerkin Pricing of American Options on Lévy Driven Assets
Last update: March 6, 2003
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Risk Management for Derivatives with Market Illiquidities

Recent turbulence on financial markets showed that risk-management models, which are based on the assumption of perfectly liquid markets, may perform very poorly if market liquidity dries up. In this RiskLab project we propose to study the hedging of derivatives in the presence of market illiquidities. Moreover, we want to analyze various strategies for the liquidation of a given position in potentially illiquid securities.
In the recent financial literature several models for markets which are not perfectly liquid have been developed. However, the practical implications of these models have not been sufficiently explored further.
The focus of our project is to:
  • Evaluate and compare existing models for market illiquidity.
  • Extend modelling of illiquidity as proposed in previous work to allow for changing market illiquidity.
  • Extend the characterization of hedging strategies by nonlinear PDE's to more advanced models for market illiquidity.
  • Implement a good and flexible numerical scheme for solving the nonlinear PDE for the hedge cost. This is a prerequisite for all subsequent analysis.
  • A detailed analysis of hedging error and hedge cost for various derivatives including certain path-dependent contracts.
  • Study the implications of market illiquidity for hedge cost and relate the results to existing pricing biases such as smiles and skews.
Current status: The numerical scheme for a nonlinear PDE has been successfully implemented; work on extended liquidity modelling, simulation-studies and implementation of hedge-simulations is in progress.
Reference: Rüdiger Frey, Market Illiquidity as a Source of Model Risk in Dynamic Hedging, pp. 125-136, in MODEL RISK, Concepts, Calibration and Pricing, edited by Prof. Rajna Gibson,Risk Books (2000), ISBN 1 899 332 898.
RiskLab researcher: Pierre Patie (25% from March 2000 until June 2001, 75% since July 2001, additional 25% supported by the Swiss Banking Institute)
Project proposal: Prof. Dr. Rüdiger Frey (Swiss Banking Institute,University of Zürich)
Contact at Swiss Re: Dr. John Hancock
Contact at UBS: George Pastrana
Related project: An Empirical Investigation on the Illiquidity in Financial Markets
Start of project: Summer 2000
Paper: Risk Management for Derivatives in Illiquid Markets: A Simulation Study
Last update: November 26, 2001
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Dependence Modelling in Risk Management

This project foresees a contribution to fundamental research in risk management (RM). The ideas will be applicable in all areas of RM (market, credit, insurance, etc.) and will be crucial to questions of risk aggregation. The project aims to establish the fundamentals of dependence and correlation modelling.
The stochastic modelling of dependent risks in the static case has essentially been completed in a RiskLab project during the residency of Daniel Straumann. A research report is available online and has been well received by practitioners and academics alike. In this follow-up project, we want to look at the following topics:
  • Simulation of dependent risks,
  • Statistical estimation of correlation in the static case,
  • Dependence and correlation in a dynamically changing environment, and
  • Extremes for heavy-tailed random vectors and multivariate stochastic processes.
The Masters thesis of Filip Lindskog, is the basis of this project. A closely related problem, namely the modelling of dependence by common shock factor models, will also be treated within this project.
RiskLab researcher: Filip Lindskog (100%)
Project proposal: Prof. Dr. Alexander McNeil (Department of Mathematics,ETH Zürich)
Contact at Swiss Re: Dr. Frank H. Krieter
Contact at UBS: John Gavin
Start of project: Middle of February 2000
Papers: Modelling Dependence with Copulas and Applications to Risk Management
Linear Correlation Estimation
Common Poisson Shock Models
Modelling Dependencies in Credit Risk Management
Kendall's Tau for Elliptical Distributions
Risk Management in Credit Risk Portfolios with Correlated Assets
Multivariate Extremes, Aggregation and Dependence in Elliptical Distributions
Last update: March 11, 2003
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Concluded Research Projects

Volatility Estimation and Risk Measurement: From Short to Long-Time Horizons

Market risk management, portfolio optimization and option pricing methods can only be as good as the model of the underlying volatility process. The aim of the project is to use intraday high-frequency financial data to improve risk measurement at long time horizons. This possibility exists because (i) volatility estimation on a time horizon of several days can be improved by the use of intra-day data, and (ii) a portfolio optimization and risk management system with portfolio re-allocation horizons of about three months is possible, if the underlying model works with time steps of the order of one week. The project is highly data-oriented. It covers the range from very short time horizons for volatility estimation to long time horizons for portfolio optimisation and risk management. In particular, the following questions will be investigated:
  • Universal method for deseasonalization of financial time series.
  • Use of high-frequency data to get better volatility estimates for different time horizons.
  • Modelling financial time series by means of a hierarchical volatility model containing a cascade from long to short time horizons.
  • Portfolio optimisation and risk management for long-time horizons.
Software and data for this project is made available by Olsen Data.
RiskLab researchers: PD Dr. Wolfgang Breymann
Dr. Céline Azizieh (visiting postdoctoral research fellow at RiskLab from Oct. to Dec. 2001)
David Mac Audière (guest from 22. 4. to 31. 7. 2002)
Project proposal: PD Dr. Wolfgang Breymann
Contact at Swiss Re: Dr. John Hancock
Contact at UBS AG: Dr. Marco Finardi (UBS Warburg)
Duration of project: September 2001 until December 2003
Paper: Dependence Structures for Multivariate High-Frequency Data in Finance
Intraday Empirical Analysis and Modelling of Diversified World Stock Indices
Reports: An Optimisation Algorithm for the Volatility Forecasting of FX Rates with the Stochastic Cascade Model
Modelling Financial Time Series with a Multifractal Model
Ph.D. Thesis: Extreme Values of Gaussian Processes and A Heterogeneous Multi Agents Model (by Christoph M. Schmid)
Software: HfFinance - An S-PLUS Tool for Deseasonalizing High-Frequency Financial Data
Forthcoming Papers: Estimation of the Stylized Facts of a Stochastic Cascade Model
A Realistic Heterogeneous Multi-Agent Model for the FX Market
Last update: April 29, 2004
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Liquidity Shocks in an Evolutionary Portfolio Theory

The purpose of this project is to introduce liquidity shocks into the new theory of portfolio selection which has recently been suggested by Hens and Schenk-Hoppé (2001). This theory is based on evolutionary reasoning in simple repeated market situations. According to this new point of view the ultimate success of a portfolio strategy is measured by the wealth share the strategy is eventually able to conquer in an evolutionary process of market selection. For the case of identical and constant savings rates, Evstigneev, Hens and Schenk-Hoppé (2001) identify a simple portfolio strategy as being the unique strategy that p-almost surely will gain the total market wealth. We want to analyze whether this neat result is robust to the more realistic case of exogenous savings that follow some stochastic process.
Project proposal: Prof. Dr. Thorsten Hens (Institute for Empirical Economic Research, University of Zürich)
Enrico De Giorgi (RiskLab)
RiskLab researcher:  Enrico De Giorgi (50%, additional 50% by IEW)
Duration of project: December 2001 until April 2003
Paper: Reward-Risk Portfolio Selection and Stochastic Dominance
Evolutionary Portfolio Selection with Liquidity Shocks
Last update: March 6, 2003
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An Empirical Investigation on the Illiquidity in Financial Markets

It is common wisdom that the standard Value-at-Risk (VaR) measure of market risk lacks rigor with respect to liquidity risk. Neglecting liquidity risk leads to underestimation of overall risk, under-capitalization, and too many violations of calculated VaR.
Attempts to quantify liquidity risk have focused both on the price impact of the execution of trades for a given portfolio (endogenous liquidity) and on portfolio-independent liquidity measures that reflect market behavior such as market spread (exogenous illiquidity). In this project, we will focus on methods for empirically quantifying exogenous liquidity risk. Our approach will lead to a liquidity VaR which incorporates a mixture of conditional market VaR and conditional (i.e. time varying) spread risk. Modeling conditional liquidity is required to yield a full integration of market and liquidity risk within a single conditional measure. Finally, we plan to go one step further and try to find variables with predictive power for market illiquidity, which could serve as an "early warning" tool for market participants, telling them when to correct their risk measures upward.
RiskLab researcher: Christian Buhl (100%, WWZ, University of Basle)
Project proposal: Prof. Dr. Heinz Zimmermann (WWZ, University of Basle)
Duration of project: April 2001 until March 2003
Related project: Risk Management for Derivatives with Market Illiquidities
Last update: April 23, 2003
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Measures of Multiperiod Risk and Time Allocation of Capital

It is very difficult to define "acceptability" for a multi-period risky project, portfolio, or position. In this work, we intend to compare different extensions of the generalized scenarios risk-measure method and evaluate the consequences in several business applications. In particular, we plan to explore:
  1. the effect that stopping due to insolvency has on a good measurement of risk;
  2. whether and how one should insist on cash-flows presentation;
  3. the idea of time allocation of capital, in particular, in the presence of several distinct projects.
As an essential part of the study, we plan to meet with practitioners to discuss various definitions of "acceptability," leaving open the possibility that different concrete problems call for different notions. Some specific issues that could be singled out include funding liquidity, transfer pricing, and the interest of diversification for a firm in the presence of regulation.
Project proposal: Prof. Dr. Philippe Artzner
RiskLab researcher: Prof. Dr. Philippe Artzner (as Visiting Research Professor)
Related previous projects: Rules of Capital Allocation (CAPA) and Coherent Measures of Risk
Coherent Allocation of the Risk Capital
Duration of project: March 2001 until February 2003
Research will continue by other means. A proposal to the Actuarial Education and Research Fund for a research grant on Multiperiod Risk Measurement in Insurance is pending.
Paper: Coherent Multiperiod Risk Measurement
Slides: Online available are 22 slides used on Nov. 25, 2002, at the Quantitative Finance Seminar, Toronto Fields Institute.
Last update: March 16, 2003
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Strategic Long-Term Financial Risks (SLTFR)

The development of a methodology that could be used for the measurement of strategic long-term financial risks is an important task. Existing modelling instruments allow for a relatively good measurement of market risks of trading books over relatively small time intervals. These models, however, have some severe deficiencies if they are applied to longer time periods.
In this project we investigate models that are proposed to be used to model the evolution of risk factors. We test these models on real data by backtesting expected shortfall predictions.
Project proposal: Swiss Re
Duration of project: Middle of November 1999 until middle of March 2003
RiskLab researchers: Roger Kaufmann (100%)
Pierre Patie (50% from March 2000 until June 2001)
Contact at Swiss Re: Dr. Niklaus Bühlmann
Dr. John Hancock
Contact at
Credit Suisse Group:		 Elisabeth Bourqui
Contact at UBS Warburg: Dr. Marco Finardi
Papers: Strategic Long-Term Financial Risks (final report including slides)
On the Normality of Long-Term Financial Log-Returns (diploma thesis)
Last update: March 15, 2003
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Credit Risk Portfolio Models

Taking into account recent insights into the means of modeling dependence structures (see Modeling Dependent Defaults by R. Frey and A. McNeil or A Risk-Factor Model for Ratings-Based Bank Capital Rules by M. B. Gordy), this project plans to determine how to design a credit portfolio model integrated in the existing market and credit risk models used by financial institutions. Some particular issues to be addressed are:
  • design of a credit portfolio model and comparison with other models used to compute economic capital,
  • comparison with intensity-based models,
  • common treatment of different products such as loans and OTC derivatives,
  • dependence between market and credit risk factors,
  • use of derivatives to mitigate eposure.
RiskLab researcher: Dr. Dirk Tasche (50%, Oct. 2001 until Feb. 2002)
Project proposal: Dr. Giovanni Cesari and Dr. Marco Finardi (both UBS AG) together with RiskLab
Duration of project: Oct. 2001 until Feb. 2002
Contact at UBS: Dr. Giovanni Cesari
Contact at
Credit Suisse Group: 		 Dr. Harry Stordel
Contact at Swiss Re: Dr. Stephan Schreckenberg
Related projects: Dependence Modelling in Risk Management
Combined Market and Credit Risk Stress Testing
Risk Modelling for a Swiss Retail/Middle Market Loan Portfolio
Last update: March 2, 2003
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Banks' Optimal Hedging Decisions Under the Threat of Bank Runs

This project will analyze a bank's risk management decision when the bank is financed with deposits and equity with limited liability. The bank is subject to the risk of depositor runs. Bankruptcy costs and regulatory restrictions are the primary motivations for risk management. Developing a model similar to Froot and Stein (1998), the optimal hedging decision will first be studied in a one-period framework. As a second step, it is planned to study the optimal hedging decision in a dynamic framework. Due to superior information, the bank earns a rent from its assets as well as from its deposits. These rents constitute the bank's franchise value. Optimal hedging strategies in the multi-period case will then be derived taking the loss of the franchise value into account in the case of bank runs.
RiskLab researcher: Wolfgang Bauer (50%, other 50% by SBI)
Project proposal: Wolfgang Bauer and Prof. Dr. Rajna Gibson (Swiss Banking Institute,University of Zürich)
Contact at
Credit Suisse Group: 		 Dr. Christian A. Walter
Duration of project: October 2001 until December 2002
Related previous project: Capital Allocation under Regulatory Constraints
Paper: Risk Management Strategies for Banks
Last update: January 29, 2003
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Risk Modelling for a Swiss Retail/Middle Market Loan Portfolio

So far credit risk modelling has concentrated largely on bonds or externally rated loans, probably mainly because of data availability. But modelling retail loans is a more important issue for loan portfolio management purposes and risk capital allocation at large retail and middle market banks (like Credit Suisse), as well as in view of the upcoming changes in the regulatory environment. The data situation (lack of long historic time series) necessitates other approaches than using market data, and the modelling approaches currently used (e.g. CreditRisk+) might not be the best available. Especially when concerned with dependence problems, there is a need to introduce macro-economic conditions into the model or linking it with market risk. The project aims to close this gap and make a potentially big contribution to modelling credit risk, also closing a gap between science and practitioners.
Research focus areas are:
  • Proper dependence modelling (versus simply using linear correlations), integrating the problems arising from the nature and data of retail portfolios.
  • Calculation of economic capital/expected shortfall and its allocation to subportfolios or even individual contracts.
  • Modelling of credit rating migration and recoverables (with proper dependence).
RiskLab researchers: Enrico De Giorgi (100%)
Filip Lindskog (partially)
Project proposal: Urs Wolf (Credit Suisse) together with RiskLab
Contact at Credit Suisse: Urs Wolf and Vlatka Komaric
Contact at UBS: Dr. Giovanni Cesari,Dr. Alexandre Kurth and Dr. Armin Wagner
References: Web page with credit risk related links
Duration of project: November 2000 until November 2001
Papers: Common Poisson Shock Models
Modelling Dependencies in Credit Risk Management
An Intensity Based Non-Parametric Default Model for Residential Mortgage Portfolios
Default Risk for Residential Mortgage Portfolios
Last update: March 29, 2004
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Capital Allocation under Regulatory Constraints

Using a stylised model similar to that of Froot and Stein (1998) the project will focus on the capital budgeting, capital structure, and risk management decisions of financial firms under regulatory constraints. The questions and issues that will be addressed in this framework are the following:
  • The introduction of the regulatory constraints as an additional rationale for risk management, as well as the analysis of how the investment, hedging, and capital budgeting decisions of financial firms are influenced by such an introduction.
  • A comparison of the influence of different forms of regulatory constraints, such as the internal models and pre-commitment approach. In the pre-commitment approach, the effectiveness of various penalty schemes could also be analysed.
  • A comparison of the influence of firm-wide regulatory constraints and separate constraints applied to trading and banking books individually.
  • The explicit introduction of a shareholder-utility maximization concept to formally study capital budgeting as opposed to custom-designed methods such as RAROC or EVA.
RiskLab researcher: Aydin Akgün (50%)
Project proposal: Prof. Dr. Rajna Gibson and Aydin Akgün (Swiss Banking Institute,University of Zürich)
Duration of project: March 2001 until August 2001
Paper: A Utility Maximization Model of Capital Budgeting with Default Risk and Regulatory Constraints
Last update: March 7, 2003
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Combined Market and Credit Risk Stress Testing

Various crisis events have demonstrated the need for financial institutions such as banks and insurance companies to perform scenario analysis under stress conditions. This goes beyond the VaR framework, which is the standard tool to estimate losses within large but not extreme market movements. Only recently new methods such as Extreme Value Theory* have been applied to model tail events.
Usually these methods are applied within a market risk environment only. Credit spreads as one of the market risk drivers are captured within the VaR framework, but no other credit effects (such as default probabilities, default correlations, and recovery rates) are taken into account.
Efforts are underway to link credit and market risk within a common modelling framework (such as models for the short interest rate that also take into account credit effects**) but these concepts have not been well established for risk management yet. The goal of this project is the development of a theoretically well-understood and empirically founded conceptual framework for a combined market and credit risk stress test methodology.
The project can be divided into the following steps:
  • Review of the literature and evaluation of existing approaches to link VaR with Credit VaR and with combined stress testing (EVT or conventional)
  • Define methodology for a combined market and credit risk stress test.
The project will be carried out in close co-operation with the industry in order to obtain solutions whose practical implementation within a sophisticated integrated risk-management system appears feasible. For this purpose the industry will designate some persons that will help to clarify the detailed needs of the industry partners within the project´s frame.
* See for example A.J. McNeil, Extreme Value Theory for Risk Managers, ETH Zurich, 1999
** See for example D.  Duffie and K. Singleton, Modeling Term Structures of Defaultable Bonds, 1999
Project proposal: Dr. Jörg Behrens and Dr. Marco Finardi (both UBS AG)
Duration of project: January 2000 until September 2001
Contact at Swiss Re: Dr. John Hancock and Marcel Rüegg
Contact at UBS: Dr. Giovanni Cesari and Dr. Christian Hauswirth
RiskLab researchers: Dr. Maria Kafetzaki Boulamatsis (60%, Jan. 2000 until Feb. 2001)
PD Dr. Nicole Bäuerle (3 weeks as visiting postdoctoral research fellow)
Dr. Dirk Tasche (5 weeks as visiting postdoctoral research fellow, 50% from April until Sep. 2001)
Report: Combined Market and Credit Risk Stress Testing Based on the Merton Model
Paper: Risk Management in Credit Risk Portfolios with Correlated Assets
Last update: March 11, 2003
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Investigation of the Market Price of Credit Risk for the Swiss Bond Market

Credit risk plays an important role in the valuation and risk management of most financial contracts. This leads to a great interest in problems of valuing credit risk - from a theoretical and practical point of view. In the nineties so-called intensity based (or reduced form) models have been developed, which assume that at each instant there is some probability that a firm defaults on its obligations. Duffie and Singleton (1995, 1997) follow this approach. Duffie (1999) tested the model for US corporations. The aim of this project is to examine how well the model of Duffie and Singleton describes corporate bond yields for the Swiss bond market and how the spread can be separated into the expected and unexpected loss. In a first step, the risk-free term structure on the basis of Swiss treasury bonds is estimated with a two-factor CIR model. Based on these results we estimate the instantaneous probability of default which follows a translated single factor square-root diffusion process, with a modification that allows for the default process to be correlated with the factors driving the default-free term structure.
RiskLab researcher: Jacqueline Henn (100%, s/bf, HSG)
Project proposal: Prof. Dr. Heinz Zimmermann (s/bf, HSG)
RiskLab support: March 2000 until March 2001
Paper: Bewertung von Kreditrisiken - empirische Untersuchungen am Schweizer Kapitalmarkt
Last update: October 9, 2001
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Rules of Capital Allocation (CAPA) and Coherent Measures of Risk

The project will compare classical as well as newer allocation rules, and evaluate their consequences for
  1. portfolio choices and strategies,
  2. performance measurement,
  3. compensation schemes.
Then, we want to investigate the following principal topics:
  1. It is important to first extend the theory of (coherent) risk measures to the multi-period case, and to compare the «rolling-over» of short-term risk measurements with a fixed long-term horizon risk measurement,
  2. then one has to systematically review the different capital allocation rules. It will be useful to describe how they are built out of risk measures and to distinguish those implying coherent risk measures from the others,
  3. given the multi-period framework and the construction of capital allocation rules via coherent risk measures, it will then be possible to detect how and why a specific rule is good at one or several of the applications mentioned above.
The following researchers, working on the same line of ideas, have contact with us: Dr. Michel Denault,Elisabeth Maignan,Dr. Uwe Schmock,Tatiana Solcà and Daniel Straumann.
Contact at UBS: George Pastrana
Duration of project: January 2000 - February 2001
Related concluded project: Coherent Allocation of the Risk Capital
Related follow-up project: Measures of Multiperiod Risk and Time Allocation of Capital
Report: Rules of Capital Allocation and Coherent Measures of Risk (CAPA)
Related work: Expected Risk-Adjusted Return for Insurance Based Models (diploma thesis)
Additionl information: Please contact Prof. Dr. Philippe Artzner or Prof. Dr. Freddy Delbaen.
Last update: March 28, 2001
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Model Risk for Credit and Market Risk Sensitive Securities

Most derivative securities are subject to market as well as credit risks. However, very few pricing and risk management models have so far integrated those two sources of risk and their interdependencies in a satisfactory way. The recent financial crises in Asia or in Russia have clearly shown that market and credit risks interact both at the macro as well as at the micro-economic levels and that they should not be managed separately.
The proposed project aims at developing a flexible pricing and hedging framework in which the market and credit risk exposures of credit-sensitive derivative securities can be simultaneously modelled. This framework should further allow us to quantify the impact of model risk on the pricing and hedging of single and aggregate derivative positions. Broadly speaking, we intend to address the following questions:
  • How to build a flexible pricing model for credit-sensitive derivatives that allows for interdependencies among market and credit risk factors?
  • How to simultaneously integrate the firm-specific and systematic components of credit risk in such a model?
  • How to refine the decomposition of the credit spreads in the general model in order to account for the business cycle characteristics of the default probabilities and of the recovery rates?
  • How to assess and quantify the model risk of nested models that do not - or, only partially - model the interaction between market and credit risks?
  • How to extend this general pricing framework for the purpose of stress-testing and assessing the validity of integrated market and credit risk management models?
RiskLab researcher: Aydin Akgün (50%)
Project proposal: Prof. Dr. Rajna Gibson (Swiss Banking Institute, University of Zürich)
Contact at UBS: Dr. Giovanni Cesari
Paper: Defaultable Security Valuation and Model Risk
Related previous project: Model Risk Management for Interest Rate Derivatives
Duration of project: April 2000 until February 2001
Last update: June 18, 2001
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Model Risk Management for Interest Rate Derivatives

In the first part of our work, we defined the model risk of hedging strategies as the law of the Profit and Loss (or of functionals of the P&L) of misspecified hedging portfolios, we explicited the P&L corresponding to various models and misspecifications - including discontinuities -, and finally we proposed an original tool to manage the model risk, namely the solution of a stochastic game problem.
For one year we worked on the theoretical and the numerical resolution of the stochastic game problem. We now have most of the desired results for one dimensional problems, and we are ready to face important questions such as the aggregation of contracts. These questions lead to delicate and new modelling problems and multidimensional stochastic control (or game) equations. If solved efficiently, they should be helpful to construct risk management techniques over large amounts of periods.
People working on the project: A thesis starting in Omega-Nancy on stochastic control equations for Insurance models is correlated to the numerical issues of our RiskLab project. As well, the RiskLab project will take benefit of the Amazone project between Omega and the French company Bull, whose objective is to develop complex numerical algorithms for financial applications on the supercomputers NEC-SX.
Papers: Modeling the Term Structure of Interest Rates: A Review of the Literature
Model Risk Analysis for Bond Options in a Heath-Jarrow-Morton Framework
Interest Rate Model Risk: What are we Talking About?
Model Risk with Jump-Diffusion Processes
Volatility Model Risk Measurement and Strategies against Worst Case Volatilities
Model Risk Management Against Worst Case Volatility Processes for Discount Bond Options
Related project: Model Risk for Credit and Market Risk Sensitive Securities
Duration of project: June 1997 until June 2000
Last update: January 10, 2001
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Dynamic Financial Analysis in Nonlife Insurance

In order to analyze the financial effects of different entrepreneurial strategies for nonlife insurance companies over a given time horizon, one finds two primary techniques in use today: The first one, the so-called scenario testing, projects results under specific deterministic scenarios in the future. The disadvantage of this approach is the fact that only a few arbitrary scenarios are tested in order to decide how good a strategy is. The other technique is stochastic simulation, better known as Dynamic Financial Analysis (DFA). Here many different scenarios are generated stochastically with the aim of giving information about the distribution of some important variables, like surplus, written premiums or loss ratio. There are lots of different versions of DFA. Our aim is not to give a comprehensive description of all of them, but rather to show the common ideas of these different models. We show how the modules of such a model can be constructed and related into an efficient complex.
RiskLab researcher: Roger Kaufmann (100%)
Project proposal: Zurich Financial Services (ZFS) and Prof. Dr. Paul Embrechts
Contact at ZFS: Andreas Gadmer and Ralf Klett
Paper: Introduction to Dynamic Financial Analysis
Duration of project: April until November 1999 (Roger Kaufmann's diploma thesis on DFA already started November 1998)
Follow-up work: Under the guidance of Roger Kaufmann, Sergi Prokopenko developed an C++ program for DFA.
Last update: September 3, 2000
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Correlation in Insurance and Finance

Insurance has traditionally been built on the assumption of independence of claims and the law of large numbers has governed the determination of premiums. An important question is: how can one incorporate dependencies? Linear correlation plays a central role in financial theory. Since the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT) are essentially based on means and variances, linear correlation proves to be a natural description of stochastic dependence, and is justified under certain distributional assumptions. However, modern risk management often places us in situations where these distributional assumptions are untenable. Moreover, we are often interested in risk measures other than variance (or standard deviation), e.g. Value-at-Risk (VaR). In this context the following question is quite natural:
  • Is linear correlation still a sufficient description of dependence?
To answer this question a better understanding of stochastic dependence is necessary. The goals of this project are:
  1. To understand dependence from a risk management point of view;
  2. To model dependence statistically.
Project proposal: Prof. Dr. Paul Embrechts and Dr. Alexander McNeil (both Department of Mathematics, ETH Zürich)
RiskLab researcher: Daniel Straumann (100%)
Paper: Correlation and Dependence in Risk Management: Properties and Pitfalls
Duration of project: January 1998 until August 1999
Follow-up project: Dependence Modelling in Risk Management
Last update: August 31, 2000
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Coherent Allocation of the Risk Capital

Much effort has been expanded in the recent years to measure the financial risks faced by a firm. Such risk measures aggregate the amounts of risk of the firm's various business units into a single number, the risk capital. However, much less effort has been devoted to the problem of allocating the risk capital back to the business units. Such an allocation is crucial for the comparison of business units on a risk-adjusted basis. The goal of this project is therefore to:
  1. investigate the basic properties that an allocation principle should display; in the spirit of a recent paper*, such properties would form the basis of a coherent allocation;
  2. to consider the coherence of currently used allocation principles; and
  3. to develop new (coherent) allocation principles. To account for the competitive relationships between the business units, some results of the theory of games are brought into play.
*Artzner, Delbaen, Eber, Heath: "Coherent measures of risk", Mathematical Finance 9 (1999), no. 3, 203-228.
Project proposal: Prof. Dr. Hans-Jakob Lüthi (IFOR, ETH Zürich)
RiskLab researcher: Dr. Michel Denault
Paper: Coherent Allocation of Risk Capital
Duration of project: June 1998 until October 1999
Related follow-up projects: Rules of Capital Allocation (CAPA) and Coherent Measures of Risk
Measures of Multiperiod Risk and Time Allocation of Capital
Last update: March 28, 2001
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Generalizations of Bessel Processes
RiskLab researcher: Dr. Anja Göing-Jaeschke
Papers: Some Generalizations of Bessel Processes (intermediate report)
Parameter Estimation and Bessel Processes in Financial Models (Part of Ph.D. thesis)
A Survey and Some Generalizations of Bessel Processes (final version)
A Clarification Note about Hitting Times Densities for Ornstein-Uhlenbeck Processes
Duration of project: October 1996 until March 1998
Last update: March 6, 2003
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Estimation in Financial Models
RiskLab researcher: Dr. Anja Göing-Jaeschke
Papers: Estimation in Financial Models (intermediate report)
Parameter Estimation and Bessel Processes in Financial Models (Part of Ph.D. thesis)
Duration of project: April 1995 until September 1996
Last update: September 19, 2000
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Risk Aggregation Techniques for Complex Financial Portfolios

The goal of this project is to develop operational measurements for the aggregated risk of portfolios of financial industries. An increasing number of complex financial instruments are being used in business today. Whereas many quantitative techniques for the analysis of a single instrument are well established, there still is a lack of mathematical methods for estimating the cumulative risk of a portfolio. New concepts, new models, and new quantitative techniques must be developed in order to aggregate the different risks of different instruments in different markets. We aim not only to determine confidence estimates for the profit and loss of a portfolio, but also to quantify these values for extreme (stress) situations. Moreover we hope to get a better understanding of the dynamic nature of risk profiles by making use of advanced mathematical modeling and simulation techniques.
RiskLab researcher: Dr. Gerold Studer
Project proposal: Prof. Dr. Hans-Jakob Lüthi (IFOR, ETH Zürich)
RiskLab reports: Value At Risk and Maximum Loss Optimization
Quadratic Maximum Loss for Risk Measurement of Portfolios
Factors at Risk
Ph.D. Thesis: Maximum Loss for Measurement of Market Risk
Papers: Maximum Loss for Risk Measurement of Portfolios
Quadratic Maximum Loss
Risk Measurement with Maximum Loss
Market Risk Computation for Nonlinear Portfolios
Last update: March 15, 2003
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Approximations of Profit-and-Loss Distributions
Papers: Approximation of P&L Distributions
Approximation of P&L Distributions, Part II
Last update: September 15, 2000
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Created and supported by Uwe Schmock until September 2003. Please send comments and suggestions to Jörg Osterrieder/ Gallus Steiger  email: finance_update@math.ethz.ch.
Last update: October 1, 2005
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