Events 2003-2004

Dr. George Hong

Risk Analyst, UBS

Modelling Forward Smile

By considering a wide class of stochastic volatility and jump models I analyse possible shapes of forward implied vol smiles and their implication for exotic derivatives pricing. A new numerical method of computing forward-start options and forward skews under affine jump diffusion stochastic vol model, generalising Carr&Madan's FFT algorithm, is presented. The method is also applicable to Levy process and stochastic time-change models and enjoys the same efficiency as in the case of vanilla options. The derivation also produces, as a by-product, a new valuation formula for variance swaps beyond the standard diffusion settings to accommodate jump risks and discrete observations. Examples of derivatives/strategies which are most sensitive to such model risks are given and discussed.

Prof. Michael Brennan

Anderson School, UCLA and Centre for Financial Research

The Dynamics of International Equity Market Expectations

This paper uses a noisy rational expectations model to derive predictions about the dynamic behaviour of the proportion of institutional money managers in a given country who are bullish about the equity markets of different countries. The predictions are tested using monthly data for four capital markets for the period October 1995 to October 2000. The empirical findings are consistent with the hypothesis of informational asymmetries between capital market participants in different countries.

Professor Mark Salmon

Financial Econometrics Research Centre, University of Warwick

Dynamic Copula Quantile Regression and Measurement of Tail Area Dependency in Forex Markets

We introduce a general approach to nonlinear quantile regression modelling that is based on the identification of the copula function that completely defines the entire dependency structure between the variables of interest. Hence we extend Koenker and Bassett's [1978] original statement of the quantile regression problem by determining a distribution for the dependent variable Y conditional on the regressors X and hence the specification of the quantile regression functions. The approach exploits the fact that the joint distribution function can be split into two parts: the marginals and the dependence function (or copula). We then deduce the form of the (non linear) conditional quantile relationship implied by the copula. Notice that this can be done with arbitrary distributions assumed for the marginals. Some properties of the copula based quantiles or c-quantiles are then derived. Finally, we develop an empirical applications which examines conditional quantile dependency in the foreign exchange market and compare this approach with the standard tail area dependency measures.

Dr Jessica James

Director, FX Advisory Group, Citigroup

Overlay and Alpha Generation Models in Foreign Exchange

In recent years the overlay industry has grown enormously as evidence accumulates that modelling the markets may yield returns. But how do the models work? Are we sure that good results are not just good fortune? This talk discusses these issues and presents a selection of commonly used FX overlay models such as trend and differential forward.

Dr Ulrich Anders

Head of Operational Risk/Head of Corporate Governance Framework, Dresdner Bank, Frankfurt

Corporate Governance and Effective Operational Risk Management

● What does 'governance' mean?
● Suggestions and contents of a governance framework
● Strategic consideration of operational risk
● Reduction of operational risks through proper governance

Professor Dr. Thorsten Hens

Centre for Financial Research, University of Cambridge, University of Zurich
Zurich Financial Services

Evolutionary Stable Stock Markets

A stock market is evolutionary stable if and only if stocks are evaluated by expected relative dividends. Any other market can be invaded by portfolio rules that will gain market wealth and hence change the valuation. In the model the valuation of assets is given by wealth average of the portfolio rules in the market. The wealth dynamics is modelled as a random dynamical system. Necessary and sufficient conditions are derived fro the evolutionary stability of portfolio rules when (relative) dividend payoffs form a stationary Markov process. These local stability conditions lead to a unique evolutionary stable strategy according to which assets are evaluated by expected relative dividends.

Dr Mark Freeman

Director of Research in Finance, School of Business and Economics, University of Exeter

Explaining the Declining Ex-ante Equity Risk

This paper describes the underlying cause of the widely reported sharp decline in the ex-ante equity risk premium during the second half of the Twentieth Century. By examining average income data for the rich, it is demonstrated that US stockholders experienced a significant reduction in economic risk around the Second World War that was recognised by investors and incorporated into stock prices by the early 1960s. This was the fundamental factor that drove the bull market of that decade. It is argued that the ex-ante risk premium has been low since the mid 1960s. Despite the reduced cost of equity capital over the last forty years, the model continues to predict hi ex-post stock returns into the 1990s, which is broadly consistent with observed market behaviour. There is only very limited evidence of excess volatility in stock returns in either half of the 1900s.

Dr William Shaw

Nomura Centre, OCIAM, University of Oxford

How can we Unify Conformal Mapping and Transform Calculus and What does it do for Mathematical Finance?

One of the less well-known corners of Laplace/Fourier transform theory is its relationship to conformal mapping of the transform variable or a mapping of the time or space variables. This seminar will begin by explaining how this works in terms of simple and elegant theorem due to Efros, and then go on to explore its applications to mathematical finance. A simplified treatment of barrier options soon emerges, and the applications of transform techniques to barrier options outside the framework of geometric Brownian motion will be presented. If time, the relationship of Asian options to conformally-mapped transforms will be discussed.

Professor Michael Dempster

Centre for Financial Research, University of Cambridge
Cambridge Systems Associates Limited

Managing Correlation Risk with Spread Options Models

● Importance of spread options in new derivatives markets
● Using spread options to hedge temporal, spatial and operations gaps
● New multifactor spread options models with stochastic correlation
● Fast pricing with fast Fourier transform techniques
● Forward correlation views and market calibration for pricing and hedging

Professor Philippe Artzner

Université Louis Pasteur, Strasbourg

Trends in multi-period risk measurement

Long term contracts (credit/Basel II, insurance/Solvency II) call specially for multi-period risk measurement, to incorporate solvency concerns into risk management. Limited liability clauses are another, supervisory, motivation for measurement. In several jurisdictions an "early warning role" is also researched.
The modelling can deal with final results of strategies or with the whole value processes. If marking to markets is not available the two approaches differ a lot.
The representation theory of one-period coherent risk measures provides specific Constructions. They coincide under the "stability" of the set of scenarios assumption which is similar to a condition met in multi-period decision theory under ambiguity.
Another approach deals only with multi-period risk of locked-in positions and allows to warn about the time inconsistency of the tail value at risk (or "expected shortfall") measurement.

Michael Villaverde

Citigroup, London

Asset Pricing with Multiple Subjective Probability Measures

This presentation describes an asset pricing framework with multiple subjective probability measures. In the one period case, assuming that agents' utility functions take a certain form results in the no strictly acceptable opportunities framework of Carr, Geman and Madan (2000). It is then shown that the framework can be thought of as a no good-deals approach. The framework is then extended to multiple periods and example implementations are presented for European call options in which the valuation bounds are shown to be considerably tighter than for no arbitrage pricing.

Anna Bermudez and Nick Webber

Cass Business School, City University

Valuing Defaultable Convertible Bonds in an Asset Based Model with Endogenised Recovery

We describe a two factor valuation model for convertible bonds when the firm may default. The underlying state variables are the asset value of the firm and the riskless short interest rate. Default can occur exogenously, or endogenously at a time a cash payment is made by the bond. We endogenize the recovery value of a defaulted bond though assumptions concerning the character of the reorganization period following default.
We use a tailored Lagrange-Galerkin discretization, coupled with a Lagrange multiplier method for free boundaries, to value convertibles in the model. Our framework enables us to specify numerically and financially consistent boundary conditions and inequality constraints.
We investigate the affect of changing the default, recovery and loss specification. The affect of introducing a stochastic interest rate is quantified, and asset and interest rate delta and gammas are found.

Dr Marco Realdon

Department of Economics & Related Studies, University of York

Valuation of Exchangeable Convertible Bonds

This paper provides a structural valuation model for exchangeable convertible bonds, since such bonds are widespread by now. The model is solved through the Hopscotch finite difference method. As the issuer owns the underlying shares, exchangeable convertibles may be called and the exchange option may be exercised even as the issuer experiences financial distress. The value of exchangeable convertibles always decreases in the volatility of the issuer's assets (unlike the value of ordinary convertibles) and decreases in the correlation between the underlying shares and the issuer's assets. The analysis confirms that the dominant motive for issuing exchangeable convertibles is likely to be to dispose of the underlying shares.

Prof. Doyne Farmer

Santa Fe Institute

Three classic problems in economics: The surprising effectiveness of zero intelligence models

Three classical problems in economics are addressed using zero intelligence models, in which agents simply make random decisions. The three problems are the nature of supply and demand, the variability of prices, and the shape of the distribution of extreme variations in prices. Also addressed are a few notquite- so classic problems, such as the origin and nature of innate transaction costs (called market friction by practitioners). The methods of analysis are drawn from statistical mechanics. The models result in simple statistical scaling laws relating order flows to prices and other properties of markets. These are tested using data from the London Stock Exchange. The fact that they match the data so well shows that, at least in some circumstances, the constraints imposed by market institutions are more important than agent rationality.

Dr. Igor Evstigneev

School of Economic Studies, University of Manchester

On the fundamental theorem of asset pricing: Random constraints and bang-bang no arbitrage criteria

This work generalizes and refines the Fundamental Theorem of Asset Pricing of Dalang, Morton and Willinger in the following two respects:
● the result is extended to a model with general portfolio constraints
● versions of the no arbitrage criterion based on the bang-bang principle in control theory are developed