Forthcoming events in this series


Thu, 21 Feb 2013

13:00 - 14:00
DH 1st floor SR

Robust Portfolio Optimization under Heavy Tailed Returns

Raphael Hauser
(Mathematics (Oxford))
Abstract

We consider the problem of optimizing a portfolio of medium to low frequency

quant strategies under heavy tailed distributions. Approaching this problem by modelling

returns through mixture distributions, we derive robust and relative robust methodologies

and discuss conic optimization approaches to solving these models.

Thu, 14 Feb 2013

13:00 - 14:00
DH 1st floor SR

Propagation of convexity and models of asset prices

Marek Musiela
(Mathematics (Oxford))
Abstract

The second order sensitivity of a trading position, the so

called gamma, has a very real and intuitive meaning to the traders.

People think that convex payoffs must generate convex prices. Being long

or short of gamma is a strategy used to balance risks in options books.

While the simples models, like Black Scholes, are consistent with this

intuition other popular models used in the industry are not. I will give

examples of simple and popular models which do not always convert a

convex payoff into a convex price. I will also give the necessary and

sufficient conditions under which the convexity is propagated.

Thu, 07 Feb 2013

13:00 - 14:00
DH 1st floor SR

On lifetime consumption and investment under a drawdown constraint

Vladimir Cherny
(Mathematics (Oxford))
Abstract

We consider a problem of maximising lifetime utility of consumption subject to a drawdown constraint on undiscounted wealth

process. This problem was solved by Elie and Touzi in the case of zero interest rate. We apply methodology of Azema-Yor processes to connect

constrained and unconstrained wealth processes, which allows us to get the results for non-zero interest rate.

Thu, 31 Jan 2013

13:00 - 14:00
DH 1st floor SR

Arrow-Debreu Equilibrium for Rank-Dependent Utility with heterogeneous Probability Weighting

Hanqing Jin
(Mathematics (Oxford))
Abstract

General Arrow-Debreu equilibrium can be determined for expected utility maximisers by explicit solutions for individual players. When the expected

utilities are distorted by probability weighting functions, players cannot find explicit optimal decisions. Zhou and Xia studied the existence of equilibrium when the probability weighting functions are the same for all individual players. In this paper, we investigate the same problem but with heterogeneous probability weighting function.

Thu, 24 Jan 2013

13:00 - 14:00
DH 1st floor SR

Volatility Estimation Using Flat-Top Realized Kernels

Rasmus Varneskov (Oxford Man Institute)
Abstract

This paper analyzes a generalized class of flat-top realized kernels for

estimation of the quadratic variation spectrum in the presence of a

market microstructure noise component that is allowed to exhibit both

endogenous and exogenous $\alpha$-mixing dependence with polynomially

decaying autocovariances. In the absence of jumps, the class of flat-top

estimators are shown to be consistent, asymptotically unbiased, and

mixed Gaussian with the optimal rate of convergence, $n^{1/4}$. Exact

bounds on lower order terms are obtained using maximal inequalities and

these are used to derive a conservative MSE-optimal flat-top shrinkage.

In a theoretical and/or a numerical comparison with alternative

estimators, including the realized kernel, the two-scale realized

kernel, and a proposed robust pre-averaging estimator, the flat-top

realized kernels are shown to have superior bias reduction properties

with little or no increase in finite sample variance.

Thu, 29 Nov 2012

13:00 - 15:00
DH 1st floor SR

How local is a local martingale diffusion?

Martin Klimmek
Abstract

Our starting point is a recent characterisation of one-dimensional, time-homogeneous diffusion in terms of its distribution at an exponential time. The structure of this characterisation leads naturally to the idea of measuring `how far' a diffusion is away from being a martingale diffusion in terms of expected local time at the starting point. This work in progress has a connection to finance and to

a Skorokhod embedding.

Thu, 22 Nov 2012

13:00 - 15:00
DH 1st floor SR

Self referential options

Jeff Dewynn
Abstract

A number of pricing models for electricity and carbon credit pricing involve nonlinear dependencies between two, or more, of the processes involved; for example, the models developed by Schwarz and Howison. The consequences of these nonlinearities are not well understood.

In this talk I will discuss some much simpler models, namely options whose values are defined self-referentially, which have been looked at in order to better understand the effects of these non-linear dependencies.

Thu, 08 Nov 2012

13:00 - 14:00
DH 1st floor SR

Economics and finance as complex systems

Doyne Farmer
Abstract

Market impact, leverage, systemic risk, and the perils of mark-to-market accounting

Market impact is the price change associated with new buy or sell orders entering the market. It provides a useful alternative to thinking in terms of supply and demand for several reasons, the most important being that there is theoretical and empirical evidence that it follows a universal law. Understanding market impact is essential for adjusting investment size, for optimizing execution tactics, and provides a useful tool for understanding market ecology and systemic risk. I will present a new method for impact-adjusted accounting, and show how it can avoid the serious problems of marking-to-market when leverage is used. Then I will discuss how market impact can be combined with network theory to understand the problem of overlapping portfolios and market crowding. Since I am a new faculty member, at the beginning of the talk I will say a bit about my interests and current projects.

Thu, 25 Oct 2012

13:00 - 14:00
DH 1st floor SR

Numerical Methods for Nash Equilibria in Multi-objective Control of Processes Governed by Partial Differential Equations

Angel Ramos
Abstract

We will discuss numerical solutions of Multi-objective Control problems governed by partial differential equations. More precisely, we will look for Nash Equilibria, which are solutions to non-cooperative differential games. First we will study the continuous case. Then, in order to compute solutions, we will combine finite difference schemes for the time discretization, finite element methods for the space discretization and a conjugate gradient algorithm (or other suitable alternative) for the iterative solution of the discrete differential game. Finally, we will apply this methodology to the solution of several test problems.

Thu, 18 Oct 2012

13:00 - 14:00
DH 1st floor SR

First Year Presentations

Tigran Atoyan, Sean Ledger, Peter Spoida
Abstract

Speaker: Tigran Atoyan\\

Title: A revised approach to hedging and pricing\\

Abstract:\\

After a brief review of the classical option pricing framework, we present a motivating example on the evaluation of hedging P&L using a simplistic strategy which does very well in practice. We then present preliminary results about a relatively unknown approach called business time hedging. Some applications of the latter approach to pricing certain derivative products as well as future research directions in this topic are discussed.\\

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Speaker: Sean Ledger\\

Title: Stochastic Evolution Equations in Portfolio Credit Modelling\\

Abstract:\\

I shall present an infinite-dimension structural model for a large portfolio of credit risky assets. As the number of assets approaches infinity we obtain a limiting system with a density process. I shall outline the properties of this density process and how one can use the SPDE satisfied by this process to estimate the loss function of the portfolio. Extensions to the model shall be onsidered, including contagion effects and Lévy noise. Finally I shall present some of the numerical testing for these models.\\

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Speaker: Peter Spoida\\

Title: Robust Pricing and Hedging of the Barrier Option with a Finite Number of Intermediate Law Constraints\\

Abstract:\\

We propose a robust superhedging strategy for simple barrier options, consisting of a portfolio of calls with different maturities and a self-financing trading strategy. The superhedging strategy is derived from a pathwise inequality. We illustrate how a stochastic control ansatz can provide a good guess for finding such strategies. By constructing a worst-case model, we demonstrate that this superhedge is the cheapest possible. Our construction generalizes the Skorokhod embedding obtained by Brown, Hobson and Rogers (2001). The talk is based on joint work with Pierre Henry-Labordere, Jan Obloj and Nizar Touzi.

Thu, 07 Jun 2012

13:00 - 14:00
DH 1st floor SR

Hybrid Modelling of Reaction, Diffusion and Taxis Processes in Biology

Radek Erban
Abstract

I will discuss methods for spatio-temporal modelling in cellular and molecular biology. Three classes of models will be considered: (i) microscopic (molecular-based, individual-based) models which are based on the simulation of trajectories of individual molecules and their localized interactions (for example, reactions); (ii) mesoscopic (lattice-based) models which divide the computational

domain into a finite number of compartments and simulate the time evolution of the numbers of molecules in each compartment; and (iii) macroscopic (deterministic) models which are written in terms of reaction-diffusion-advection PDEs for spatially varying concentrations. In the first part of my talk, I will discuss connections between the modelling frameworks (i)-(iii). I will consider chemical reactions both at a surface and in the bulk. In the second part of my talk, I will present hybrid (multiscale) algorithms which use models with a different level of detail in different parts of the computational domain. The main goal of this multiscale methodology is to use a detailed modelling approach in localized regions of particular interest (in which accuracy and microscopic detail is important) and a less detailed model in other regions in which accuracy may be traded for simulation efficiency. I will also discuss hybrid modelling of chemotaxis where an individual-based model of cells is coupled with PDEs for extracellular chemical signals.

Thu, 17 May 2012

13:00 - 14:00
DH 1st floor SR

Quick Computation of Upper and Lower bounds for Discretised Min-Max Equations

Jan Witte
Abstract

Min-Max equations, also called Isaacs equations, arise from many applications, eg in game theory or mathematical finance. For their numerical solution, they are often discretised by finite difference

methods, and, in a second step, one is then faced with a non-linear discrete system. We discuss how upper and lower bounds for the solution to the discretised min-max equation can easily be computed.

Thu, 10 May 2012

13:00 - 14:00
DH 1st floor SR

Pro-Rata Matching and One-Tick Futures Markets

Jeremy Large
Abstract

We find and describe four futures markets where the bid-ask spread is bid down to the fixed price tick size practically all the time, and which match coun- terparties using a pro-rata rule. These four markets’ offered depths at the quotes on average exceed mean market order size by two orders of magnitude, and their order cancellation rates (the probability of any given offered lot being cancelled) are significantly over 96 per cent. We develop a simple theoretical model to explain these facts, where strategic complementarities in the choice of limit order size cause traders to risk overtrading by submitting over-sized limit orders, most of which they expect to cancel.

Joint work with Jonathan Field.

Thu, 08 Mar 2012
13:00
DH 1st floor SR

Pertubative method for quadratic reflected backward stochastic differential equations

Arnaud Lionnet
Abstract

In this talk, I will present reflected backward stochastic differential equations (reflected BSDEs) and their connection with the pricing of American options. Then I will present a simple perturbative method for studying them. Under the appropriate assumptions on the coefficient, the terminal condition and the lower obstacle, similar to those used by Kobylankski, this method allows to prove the existence of a solution. I will also provide the usual comparison theorem and a new proof for a refined comparison theorem, specific to RBSDEs.

Thu, 02 Feb 2012
13:00
DH 1st floor SR

Uncertainty and nonlinear expectations

Sam Cohen
Abstract

Decision making in the presence of uncertainty is a mathematically delicate topic. In this talk, we consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering discrete-time `martingale' processes, we show that the classical results of martingale convergence and the up/downcrossing inqualities hold in a `quasi-sure' sense. We also give conditions, for a general filtration, under which an `aggregation' property holds, generalising an approach of Soner, Touzi and Zhang (2011). From this, we extend various results on the representation of conditional sublinear expectations to general filtrations under uncertainty.

Thu, 26 Jan 2012
13:00
DH 1st floor SR

Some recent findings in the computation of American option prices

Christoph Reisinger
Abstract

In this seminar, we discuss three questions related to the finite difference computation of early exercise options, one of which has a useful answer, one an interesting one, and one is open.

We begin by showing that a simple iteration of the exercise strategy of a finite difference solution is efficient for practical applications and its convergence can be described very precisely. It is somewhat surprising that the method is largely unknown.

We move on to discuss properties of a so-called penalty method. Here we show by means of numerical experiments and matched asymptotic expansions that the approximation of the value function has a very intricate local structure, which is lost in functional analytic error estimates, which are also derived.

Finally, we describe a gap in the analysis of the grid convergence of finite difference approximations compared to empirical evidence.

This is joint work with Jan Witte and Sam Howison.