Download Financial Mathematics and Applied Probability Seminars 2003-2004

Financial Mathematics and Applied Probability Seminars 2003-2004
Unless indicated, all seminars take place at Lecture Theatre 2C, King's College London,
The Strand, London WC2R 2LS.
Tuesday 30 Professor Angus MacDonald
September, Director, Genetics and Insurance Research Centre, Department of Actuarial Mathematics and
5:30 pm Statistics, Heriot-Watt University
Genetics and Insurance: Data and Models
Abstract: According to the media, genetics and insurance just cannot live together: if
insurance companies can access any genetic (medical) information about people who
apply for life or health insurance, the world will divide into those who will never fall
ill (insurable) and those who will definitely fall ill (uninsurable). Simple mathematical
models, plus some genetic epidemiology, show how unlikely this is, but despite the
fact that this has been in the public domain for several years the media never learns:
every time genetics and insurance becomes an issue we seem to be back to square
one. This talk will outline actuarial models for exploring the financial consequences
of genetics, for individuals and for insurers.
Tuesday 7 Dr William Shadwick
October, The Finance Development Centre Limited, London
5:30 pm Omega Functions and Analysis of Financial Data
Abstract: The Omega function of a univariate probability distribution is, like the
probability density function, characteristic function or moment generating function
(when one exists), another mathematically equivalent way of encoding the
information in the distribution. It is particularly well suited to the analysis of
properties of tails and asymmetries of distributions. As a result, it provides significant
new insights into those risk/reward characteristics of financial instruments which are
ignored by conventional mean/variance tools and only partially captured by skew
and kurtosis.
Unlike the alternative descriptions of a distribution listed above, the Omega function
was only recently discovered, although it requires no mathematical technology
which was not available to Gauss. I will give an introduction to Omega functions and
some of their intriguing mathematical properties, followed by examples of the impact
of applying this new approach real financial data. These will be accompanied by
some graphical illustrations which require rather more computational power than
even Gauss would likely have been able to muster.
(Joint work with Ana Cascon, Con Keating and Brad Shadwick)
Tuesday 21 Professor Claudio Albanese
October, Department of Mathematics, University of Toronto, Canada
5:30 pm Discretization Schemes for Option Pricing Models with Jumps and State-dependent
Volatility
Abstract: I introduce a Poisson approximation scheme for jump processes with state-
dependent local volatility and use it to construct arbitrage-free discretization schemes
for the corresponding pricing PIDEs. The crucial property of these lattice models is
their great stability, as one can set the time nodes at arbitrary dates without affecting
the end-result for the price of European options. This is achieved by computing
node-to-node transition probabilities analytically as expansions in hypergeometric
polynomials. I outline applications of this technique to equity and credit derivatives.
Tuesday 28 Dr Arne Lokka
October, Department of Mathematics, University of Oslo
5:30 pm Equilibrium and incomplete financial markets
Abstract: A financial market is in equilibrium if there is a balance between the supply
and the demand for assets. If the market is complete, there exists a unique pricing
rule determining the price of every asset. What happens when the market is
incomplete? In my talk I will try to give some answers to this question.
Tuesday 11 Professor Mark Davis
November, Department of Mathematics, Imperial College London
5:30 pm An optimal investment problem with randomly terminating income
Abstract: Optimal investment with 'random endowment' is an important topic
because of the connection with asset valuation and hedging of liabilities in
incomplete markets. In this talk we revisit Merton's classic problem of maximizing
utility of consumption over an infinite time horizon when asset prices are log-normal.
Merton already noted how to adapt the solution to accommodate a known income
stream, and a similar argument applies to any hedgeable income stream. When the
income is not hedgeable the situation is much more complicated. We study a specific
problem by duality methods. The dual minimization problem is one of deterministic
optimal control, for which we obtain a computable solution.
This is joint work with Michel Vellekoop.
On Mark Davis' website there are slides of this talk available.
Tuesday 25 Dr Mark Joshi
November, Quantitative Research Centre, Royal Bank of Scotland
5:30 pm Rapid and Accurate Computation of Prices and Greeks for Basket Credit Default
Swaps in the Li Model
* The Li model for pricing basket credit default swaps
* Using importance sampling
* Difficulties in computing sensitivities
* The likelihood ratio method
* The pathwise method applied to discontinuous pay-offs
* Numerical results
Tuesday 20 Dr Dirk Becherer
January,
5:30 pm
Department of Mathematics, Imperial College London
On futures prices in supermartingale term structure models
Abstract: The talk is on general futures prices in the framework of supermartingale
pricing kernel models. We show how recent results on supermartingale term
structure models plus stochastic backward integration allow for a unifying view on
discretely and continuously resettled contingent claims, and discuss the structure
behind the natural numeraires for obtaining the futures price process.
Email the speaker: dirk.becherer(at)imperial(.)ac(.)uk
Website of the speaker
Tuesday 27 Professor Alex Kacelnik
January, Department of Zoology, Oxford University
5:30 pm Behavioural Risk Sensitivity in animals and humans: from the beginnings to Scalar
Utility Theory
Abstract: The consequences of most actions are stochastic, that is, they entail some
risk. The problem of how risk relates to decision making has been faced by
economists for centuries, by psychologists for a long time and by biologists
researching non-human behaviour for a couple of decades. Their findings and
theoretical frameworks show important similarities as well as differences. Economists
and psychologists have given strong emphasis to risk aversion, its possible rationality
and its psychological causes. In contrast, evolutionary biologists faced risky choice
from a theoretical standpoint that assumes evolutionary rationality and statedependency, leading to predictions of either risk-seeking or risk-avoidance
depending on the state and payoff representation of the subject. Reality, however, is
unique, and empirical work is forcing these approaches to converge. I shall outline
classical economic views (Bernoulli), Prospect theory (Kahneman); Risk Sensitivity
Theory (Caraco, Houston & McNamara) and Scalar Utility Theory (my own pet
account) and review some of the relevant empirical evidence.
Kacelnik A & Bateson M (1997) Risk-sensitivity: cross-roads for theories of decision
making. Trends in Cognitive Sciences 1, 304-309.
Kacelnik A & Brito e Abreu F. (1998) Risky Choice and Weber¹s Law. J.
Theoretical Biology 194, 289-298
Website of Alex Kacelnik's ecology research group in Oxford.
Tuesday 3 Professor Ragnar Norberg
February, Department of Statistics, London School of Economics
5:30 pm Vasicek beyond the normal
Abstract: A general Ornstein-Uhlenbeck (OU) process is obtained upon replacing
the Brownian motion appearing in the defining stochastic differential equation with a
general Levy process. Certain properties of the Brownian ancestor are distributionfree and carry over to the general OU process. Explicit expressions are obtainable for
expected values of a number of functionals of interest also in the general case. Special
attention is paid here to gamma and Poisson driven OU processes. The Brownian,
Poisson, and gamma versions of the OU process are compared in various respects
and, in particular, their aptitude to describe stochastic interest rates is discussed in
view of some standard issues in financial and actuarial mathematics; prices of zerocoupon bonds, moments of present values, and probability distributions of present
values of perpetuities. The problem of possible negative interest rates finds its
resolution in the general set-up by taking the driving Levy process to be nondecreasing (a subordinator).
The talk will be based on the paper Vasicek beyond the normal.
Email the speaker.
The speaker's homepage.
Tuesday 10 Dr Gael Martin
February, Department of Econometrics and Business Statistics, Monash University, Australia
5:30 pm Bayesian Estimation of a Stochastic Volatility Model Using Option and Spot Prices:
Application of a Bivariate Kalman Filter
Abstract: In this paper we apply Bayesian methods to estimate a stochastic volatility
model using both the prices of the asset and the prices of options written on the
asset. Implicit posterior densities for the parameters of the volatility model, for the
latent volatilities and for the market price of volatility risk are produced. The method
involves augmenting the data generating process associated with a panel of option
prices with the probability density function describing the dynamics of the
underlying bivariate spot price and volatility process. Posterior results are produced
via a hybrid Markov Chain Monte Carlo sampling algorithm. Candidate draws for
the unobserved volatilities are obtained via the application of the Kalman filter and
smoother to a linearization of the non-linear state-space representation of the model.
Crucially, information from both the spot and option prices affects the draws via the
specification of a bivariate measurement equation. The method is illustrated using
the Heston (1993) stochastic volatility model, applied to spot and option price data
on Australian News Corporation stock data. The way in which alternative option
pricing models nested in the Heston framework can be ranked, via Bayes Factors
and via fit, predictive and hedging performance, is also demonstrated.
(Joint work with Catherine Forbes and Jill Wright.)
Tuesday 24 No seminar planned due to AUT strike
February,
5:30 pm
Tuesday 16 Professor Vicky Henderson
March,
Bendheim Center for Finance, Princeton University
5:30 pm Valuing Real Options without a Perfect Spanning Asset
Abstract: The real options approach to corporate investment decision making
recognizes a firm can delay an investment decision and wait for more information
concerning project cashflows. The classic model of McDonald and Siegel (1986) (see
also Dixit and Pindyck (1994)) values the investment decision as a perpetual
American option and in doing so, essentially assumes the real asset underlying the
option is traded, or that there is a perfect spanning asset available. Most real projects
however can only be partially hedged by traded securities. Our model relaxes this
assumption and assumes only a partial spanning asset can be found.
In this model, we obtain in closed form the value of the option to invest and the
optimal investment trigger level, above which investment takes place. These both
depend on the correlation between project cashflows and the spanning asset, risk
aversion of the firm's shareholders, and volatilities of project cashflows and the partial
spanning asset. We observe that the value of the option to invest and the trigger
level are both lowered when the spanning asset is less than perfect. This implies the
firm should invest earlier than the classic models suggest.
Although the partial spanning model contains the classic model as a special case, it is
much richer. In particular, there are situations where the classic model recommends
the firm always postpones investment, whereas if a highly (but not perfectly)
correlated spanning asset were assumed, the firm should invest at a certain trigger
level.
Tuesday 23 Dr Tony He
March,
School of Finance and Economics, University of Technology, Sydney
5:30 pm Asset Pricing, Volatility and Market Behavior ---A Market Fraction Approach
Abstract: Motivated by recent development in structural agent models on asset
pricing, explanation power and calibration issue of those models, this paper presents
a simple market fraction model of two types of traders---fundamentalists and trend
followers---under a market -maker scenario. It is found that asset prices, wealth
dynamics and market behaviors are characterized by the dynamics of the underlying
deterministic system. The model is able to explain various market behaviors, and to
generate some of the stylized facts. By introducing two measures on wealth
dynamics, we are able to show the limitations of profitability and rationality of
different trading strategies. Six significant autocorrelation coefficient (ACs) patterns
are characterized by different types of bifurcation of the underlying deterministic
system. In particular, an oscillating and decaying AC pattern with positive ACs for
even lags and negative for odd lags can be generated when the market is dominated
by the fundamentalists (that is when the parameters are near the flip bifurcation
boundary), and a positive decaying AC patterns with long memory can be generated
when the market is dominated by the trend followers with high decay memory (that
is when the parameters are near the Hopf bifurcation boundary). The results show a
promising power of stability analysis and bifurcation theory in explaining and
calibrating asset price and wealth dynamics, market behavior, and generating various
econometric properties of financial data.
The full paper can be downloaded here.
Email the speaker
Website of the School of Finance and Economics, University of
Technology, Sydney.
Tuesday 30 Professor Onesimo Hernandez-Lerma
March,
Departamento de Mathematicas, CINVESTAV-IPN, Mexico
5:30 pm Topics in optimal control and game theory
Room 17B
Topics in optimal control and game theory
Professor Onesimo Hernandez-Lerma, Departamento de Mathematicas, CINVESTAV-IPN,
Mexico
Abstract: Optimal control and game theory are very active research fields partly
because they provide a rich source of complex mathematical problems, and partly
because of their applicability in such diverse areas as engineering, economics,
finance, and (renewable and nonrenewable) resource management, to name a few.
This talk is a nontechnical introduction, mainly via examples, to some topics in
control and game theory, including adaptive control, minimax control (a.k.a. "worstcase control" or "games against nature"), partially observable systems (a.k.a. "hidden
Markov models"), cooperative and noncooperative game equilibria, etc.
Email the speaker.
Tuesday 20 Professor Raymond Brummelhuis
April,
Department of Mathematics and Statistics, Birkbeck College, London
5:30 pm Multi-period risk assesment in GARCH models
Abstract: A question of common interest is how to evaluate multiple period Value at
Risk in heteroscedastic models like GARCH(1, 1). For example, in the context of
the Basle agreement, how to the estimate the 10-day 99% VaR on the basis of a
GARCH model for the daily returns. We discuss some approaches to this question,
both numerical and theoretical. We will in particular study ways to quantify the
intertemporal dependence structure in a GARCH(1, 1 ), by introducing and
evaluating suitably defined tail dependence functions and coefficients, which are a
variant on the usual coefficient of (lower) tail dependence.
Tuesday 11 Dr Pauline Barrieu
May,
Department of Statistics, London School of Economics
5:30 pm Optimal derivatives design under dynamic risk measures
Talk will be based on the paper Optimal derivatives design under dynamic risk
measures, written jointly with Nicole El Karoui and to be published on the
Proceedings of the AMS in spring 2004.
Tuesday 18 Dr Robert Tompkins
May,
Business school of Finance and Management (HfB), Germany,
5:30 pm Unconditional Return Disturbances: a Non Parametric Simulation Approach
Abstract: Simulation methods are extensively used in Asset Pricing and Risk
Management. The most popular of these simulation approaches, the Monte Carlo,
requires model selection and parameter estimation. In addition, these approaches can
be extremely computer intensive. Historical simulation has been proposed as a nonparametric alternative to Monte Carlo. This approach is limited to the historical data
available.
In this paper, we propose an alternative historical simulation approach. Given a
historical set of data, we define a set of standardized disturbances and we generate
alternative price paths by perturbing the first two moments of the original path or by
reshuffling the disturbances. This approach is totally non parametric when constant
volatility is assumed, or semi-parametric in presence of GARCH (1,1) volatility and is
shown without a loss in accuracy to be much more powerful in terms of computer
efficiency than the Monte Carlo approach. This approach is extremely simple to
implement and is shown to be an effective tool for the valuation of financial assets.
We apply this approach to simulate pay off values of options on the S&P 500 stock
index for the period 1982-2003. To verify that this technique works, the common
back-testing approach was used. The estimated values are insignificantly different
from the actual S&P 500 options payoff values for the observed period.
This is joint work with Rita L. D'Ecclesia, University of Rome "La Sapienza".
JEL classifications: C15, G13, G19
Email the speaker: [email protected] or [email protected].
Tuesday 15 Dr Damien Challet
June,
Nomura Centre for Quantitative Finance, Mathematical Institute, Oxford
5:30 pm The quest for large and small fluctuations in minority games: financial and
technological applications
Abstract: We first provide two alternative explanation on the relevance of Minority
Games to financial markets. Then we build various models of financial markets on
one of them, extending thebasic Minority Games to new realms. Under what
conditions large price fluctuations arise in these models will be the central part of my
talk.
Whereas one expects financial market models to produce large fluctuations, small
fluctuations are a better outcome in a technological setting, for instance in the case of
Internet routers trying to transmit efficiently packages. The second part of my talk
proposes new stochastic strategies for the basic Minority Game that lead to minimal
fluctuations.