Past Mathematical Finance Internal Seminar

9 May 2014
13:00
Owen Jones
Abstract
Traditional diffusion models for random phenomena have paths with Holder regularity just greater than 1/2 almost surely but there are situations arising in finance and telecommunications where it is natural to look for models in which the Holder regularity of the paths can vary. Such processes are called multifractal and we will construct a class of such processes on R using ideas from branching processes. Using connections with multitype branching random walk we will be able to compute the multifractal spectrum which captures the variability in the Holder regularity. In addition, if we observe one of our processes at a fixed resolution then we obtain a finite Markov representation, which allows efficient simulation. As an application, we fit the model to some AUD-USD exchange rate data. Joint work with Geoffrey Decrouez and Ben Hambly
  • Mathematical Finance Internal Seminar
14 March 2014
13:00
Harald Oberhauser
Abstract
The question of how to derive useful bounds on arbitrage-free prices of exotic options given only prices of liquidly traded products like European call und put options has received much interest in recent years. It also led to new insights about classic problems in probability theory like the Skorokhod embedding problem. I will take this as a starting point and show how this progress can be used to give new results on general Monte-Carlo schemes.
  • Mathematical Finance Internal Seminar
28 February 2014
13:00
Jan Obloj
Abstract
I explore some new ideas on embedding problems for Brownian motion (and other Markov processes). I show how a (forward) Skorokhod embedding problem is transformed into an optimal stopping problem for the time-reversed process (Markov process in duality). This is deduced from the PDE (Variational Inequalities) interpretation of the classical results but then shown using probabilistic techniques and extended to give an n-marginal Root embedding. I also discuss briefly how to extend the approach to other embeddings such as the Azema-Yor embedding.
  • Mathematical Finance Internal Seminar
21 February 2014
13:00
Peng Hu
Abstract
The aim of this lecture is to give a general introduction to the interacting particle system and applications in finance, especially in the pricing of American options. We survey the main techniques and results on Snell envelope, and provide a general framework to analyse these numerical methods. New algorithms are introduced and analysed theoretically and numerically.
  • Mathematical Finance Internal Seminar
31 January 2014
13:00
Alex Cox
Abstract
We consider the pricing of American put options in a model-independent setting: that is, we do not assume that asset prices behave according to a given model, but aim to draw conclusions that hold in any model. We incorporate market information by supposing that the prices of European options are known. In this setting, we are able to provide conditions on the American Put prices which are necessary for the absence of arbitrage. Moreover, if we further assume that there are finitely many European and American options traded, then we are able to show that these conditions are also sufficient. To show sufficiency, we construct a model under which both American and European options are correctly priced at all strikes simultaneously. In particular, we need to carefully consider the optimal stopping strategy in the construction of our process. (Joint with Christoph Hoeggerl).
  • Mathematical Finance Internal Seminar

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