Beyond Part III

Young Researchers in Mathematics 2009

16-18 April 2009

Centre for Mathematical Sciences, Cambridge

Quantitative Finance Session

Talks will be in MR12, except for Friday 11.45-12.30 (MR2).



Scenario generation for interest rate models and derivative pricing - Omri Ross

The correct way of modelling interest rates (IR) depends on the actual use of the model. Central banks and long term investors, such as pension funds, can be interested in models that capture the trends in interest rates in order to identify the current economic state and inflation. Trading desks and market makers will be interested in models that can price derivatives accurately in accordance with the market price in order to structure IR derivatives and be able to identify market mispricing as well as to outperform their competitors.

The overview of interest rate models is developed in essentially chronological order. It starts from one factor spot rate models and develops multi-factor spot rate affine models. These models account for different shapes of the yield curve but generally do not match the initial yield curve and therefore are hard to use for short term trading purposes. Thus, these models can be used for structuring and selling OTC products in cases where the sales fee is above 2% of the contract and for issuing a long term contract where the long term value of the economic cycle is more meaningful than the short term trend.

A short discussion of using these models for stochastic programming applications will follow as we are interested in applying methods to generate and solve multi-stage stochastic programming application for asset liability management.

Finally an in depth case study describing a three factor term structure model and a discussion of the risk and payout distributions of different interest rate derivatives will be discussed.

Large Deviations theory for Implied Volatility Asymptotics - Antoine Jacquier

Using Large Deviations Theory, and in particular the Gartner-Ellis theorem, we characterise the leading-order behaviour of call option prices and implied volatilities under the Heston model for small and large maturities. In this context we also show how to derive similar results if we add an independent Levy component to the stock price process. In the large maturity regime, we can make this statement even more precise by providing the first-order behaviour using Cauchy's theorem and Saddlepoint Approximations. This talk is based on several joint papers with Martin Forde.

Credit Modelling by Particle System and SPDE - Lei Jin

In this talk, we try to construct a model in the credit market under the structural-model framework. We use the particle representation for the firms' asset value and investigate the behavior of the empirical measure of the particle system. By proving the convergence of the empirical measure we can achieve an explicit description of the limit empirical measure and calculate the default proportion at any time t. Furthermore, the dynamics of the underlying firms' asset values can be assumed to be either driven by Brownian motions or more general Levy processes, or even have some interactive effects among the particles.

This is a joint work with Dr. Ben Hambly, University of Oxford.

Hedging in large financial markets - Mike Tehranchi (keynote speaker)

After some preliminaries on financial mathematics, I will discuss how a large financial market can be modeled via a stochastic evolution equation in an infinite dimensional space. In the context of such a model, the issue of hedging can be studied in terms of a martingale representation theorem. The specific topic of hedging exotic equity derivatives with a portfolio of variance swaps will be treated as an example. This work is joint with Francois Berrier.

Mathematics in Finance (accessible talk) - James Holloway

I will talk about the uses and abuses of mathematics in finance. In particular, how the poor understanding of modelled risk (i.e. statistics) has led to the current crisis. I will also talk about the Efficient Market Hypothesis, and how its blind application as a mathematical axiom is wrong. This will be a talk that anyone from any discipline can attend (I am, after all, a physicist), and it won't be too dry!

Modelling asymmetric and fat tails by quantile autoregression (QAR) - Roberto Bustreo

The presentation is showing properties of quantile regression, applying it to time series. The Quantile AutoRegression model is then presented and data modelling is carried out using AIC criterion. Some empirical applications are shown.