Friday, October 22, 1999, 9.00 - 17.00
Conference program and abstracts are available online.
|9.00 - 9.30||Prof. Dr. Paul Embrechts
(Dept. of Math. and
Teaching and Research in Insurance and Finance in Zurich
Abstract: We give a short overview of the activities in Financial and Insurance Mathematics in Zurich, in particular the education in actuarial mathematics and the finance research centre RiskLab.
|9.30 - 10.00||Dr. Uwe Schmock
Dept. of Math.,
Allocation of Risk Capital and Performance Measurement
Abstract: Allocation of the risk bearing capital to the business units of a financial institution is an important tool for performance measurement, risk control and steering of the company. Allocation principles for risk capital are also applicable to portfolios of defaultable bonds or credit risks. We shed some light on the advantages and shortcomings of allocation principles, in particular the Euler principle, the covariance and the expected shortfall principle, which all take dependencies into account. In addition, we show how the capital allocation can be calculated in practice, for example for dependent risk processes. (Joint work with Daniel Straumann, RiskLab.)
|10.00 - 10.30||Dr. Michel Denault
Coherent Allocation of Risk Capital
Abstract: We introduce the concept of coherence of the allocation. Risk measurement and capital allocation are two distinct problems; after Artzner, Delbaen, Eber and Heath defined their coherent risk measure by establishing necessary properties of risk measures, we transposed their approach to the problem of allocation, and set out the properties that an allocation principle should possess.
|10.30 - 11.00||Coffee Break|
|11.00 - 11.30||Dr. Alexander McNeil
(Dept. of Math.,
Correlation and Dependence in Risk Management
Abstract: Modern risk management calls for an understanding of stochastic dependence going beyond simple linear correlation. We deal with the static (non-time-dependent) case and emphasize the copula representation of dependence for a random vector. Linear correlation is a natural dependence measure for multivariate normally and, more generally, elliptically distributed risks but other dependence concepts like comonotonicity, rank correlation and tail dependence should also be understood by the risk management practitioner. Using counterexamples the falsity of some commonly held views on correlation is demonstrated; in general, these fallacies arise from the naive assumption that dependence properties of the elliptical world also hold in the non-elliptical world. In particular, the problem of finding multivariate models that are consistent with prespecified marginal distributions and correlations is addressed. Pitfalls are highlighted and simulation algorithms avoiding these problems are mentioned. (Based on joint work with Paul Embrechts and Daniel Straumann, RiskLab.)
|11.30 - 12.00||Roger Kaufmann
Dept. of Math.,
Dynamic Financial Analysis
Abstract: For analyzing the financial effects of different strategies for insurance companies over a given time horizon, there are two primary techniques in use today: the first, so-called scenario testing, projects results under a few specific scenarios in the future. 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 or loss ratio. In this talk it will be explained how DFA works.
|12.00 - 13.50||Lunch Break|
|13.50 - 14.20||Vicky Henderson
(University of Bath,
future member of
Passport Options - A Tool for Fund Managers
Abstract: A passport option, as introduced and marketed by Bankers Trust, is a call option on the balance of a trading account. The strategy that this account follows is chosen by the option holder, subject to position limits. This option can be thought of as a type of capital-guaranteed product for fund managers and we discuss some relevant extensions which make it useful for these purposes.
|14.20 - 14.50||Marco Jost
(Dept. of Math.,
Microstructure of Order Book Trading Markets
Abstract: The interest in a better understanding of market microstructure has grown considerably recently, especially with the availability of high frequency data. But the theory developed so far fits rather badly to the double auction mechanism of markets, where trading is done via an order book. We therefore are concerned with more appropriate models and will show that even for a quite simplistic behaviour of the agents, the resulting equilibrium price process reveals some interesting features.
|14.50 - 15.20||Patrick Cheridito
(Dept. of Math.,
Long-Range Dependence and Option Pricing
Abstract: Several attempts have been made to remedy some shortcomings of the Black-Scholes model by describing the risky asset as a process with dependent increments. Fractional Brownian motion is a Gaussian process that exhibits long-range dependence between the increments, but it is not a semi-martingale. In the talk arbitrage strategies for fractional models are presented. But since they consist of ever faster buying and selling, they only exist as mathematical integrands without economic meaning and can be excluded by regularizing the local behaviour of fractional Brownian motion. This leads to a class of arbitrage-free, complete option pricing models with long-range dependence.
|15.20 - 16.00||Coffee Break|
|16.00 - 16.30||Prof. Dr. Rüdiger Frey
(Swiss Banking Institute,
University of Zürich)
The Hedging of Derivatives in the Presence of Market Illiquidities
Abstract: In standard derivative asset analysis it is assumed that the seller of a derivative contract is a price taker on the market for the underlying asset. Here we depart from this assumption and consider a model where the implementation of a hedging strategy affects the price of the underlying security. We derive a formula for the feedback-effect of dynamic hedging on market volatility and characterize perfect hedging strategies by a nonlinear version of the Black-Scholes PDE. We give a new economic interpretation to a first order approximation to this PDE. Simulations are used to quantify the additional hedge cost due to market illiquidity.
|16.30 - 17.00||Prof. Dr. Rajna Gibson
(Ecole des HEC,
University of Lausanne,
future member of the
Swiss Banking Institute,
University of Zürich)
Model Risk Analysis for Bond Options in a Heath-Jarrow-Morton Framework
Abstract: In this talk, we analyze model risk for discount bond options within a univariate HJM (1992) framework and show analytically how to express the agents' model risk profit and loss as a function of the position's gamma. We further provide mathematical results on the distribution of the forward profit and loss function for some specific univariate term structure models. Finally, we run numerical simulations for elementary and more complex options' hedging strategies in order to examine the sensitivity of the P&L function with respect to the volatility of the forward rate curve, the shape of the term structure and the characteristics of the position being hedged. (Joint work with M. Bossy, F. Lhabitant, N. Pistre and D. Talay.)
Local Organizers: Paul Embrechts, Rüdiger Frey, Uwe Schmock,
Conference Secretary: Mrs G. Baltes, HG G37.2, Phone 01/632 34 00, E-mail: email@example.com
Other Risk Days: 1998, 2000, 2001, 2002, 2003, 2004