Past Mathematical Finance Internal Seminar

26 November 2009
13:00
Alok Gupta
Abstract
We investigate calibrating financial models using a rigorous Bayesian framework. Non-parametric approaches in particular are studied and the local volatility model is used as an example. By incorporating calibration error into our method we design optimal hedges that minimise expected loss statistics based on different Bayesian loss functions determined by an agent's preferences. Comparisons made with the standard hedge strategies show the Bayesian hedges to outperform traditional methods.
  • Mathematical Finance Internal Seminar
15 October 2009
13:00
Sergey Nadtochiy
Abstract
Most financial models introduced for the purpose of pricing and hedging derivatives concentrate on the dynamics of the underlying stocks, or underlying instruments on which the derivatives are written. However, as certain types of derivatives became liquid, it appeared reasonable to model their prices directly and use these market models to price or hedge exotic derivatives. This framework was originally advocated by Heath, Jarrow and Morton for the Treasury bond markets. We discuss the characterization of arbitrage free dynamic stochastic models for the markets with infinite number of European Call options as the liquid derivatives. Subject to our assumptions on the presence of jumps in the underlying, the option prices are represented either through local volatility or through local L´evy measure. Each of the latter ones is then given dynamics through an Itˆo stochastic process in infinite dimensional space. The main thrust of our work is to characterize absence of arbitrage in this framework and address the issue of construction of the arbitrage-free models.
  • Mathematical Finance Internal Seminar
11 June 2009
13:00
Alison Etheridge
Abstract
We take a leisurely look at some mathematical models from population genetics and the ways that they can be analysed. Some of the models have a very familiar form - for example diffusion models of population size look a lot like interest rate models. But hopefully there will also be something new.
  • Mathematical Finance Internal Seminar
28 May 2009
13:00
Lei Jin
Abstract
In this talk, we try to construct a dynamical model for the basket credit products in the credit market under the structural-model framework. We use the particle representation for the firms' asset value and investigate the evolution of the empirical measure of the particle system. By proving the convergence of the empirical measure we can achieve a stochastic PDE which is satisfied by the density of the limit empirical measure and also give an explicit formula for 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.
  • Mathematical Finance Internal Seminar
14 May 2009
13:00
Zhongmin Qian
Abstract
This talk will be based on a joint work with Professor Terry Lyons and Mr Gechun Liang (OMI). I will explain a new approach to define and to solve a class of backward dynamic systems including the well known examples of non-linear backward SDE. The new approach does not require any kind of martingale representation or any specific restriction on the probability base in question, and therefore can be applied to a much wider class of backward systems.
  • Mathematical Finance Internal Seminar

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