Mathematical Finance Internal Seminar (past)
|
Thu, 16/05 13:00 |
Ben Hambly |
Mathematical Finance Internal Seminar  |
DH 1st floor SR |
| I will look at a toy model for an index in a large market. The aim is to consider the pricing of volatility swaps on the index. This is very much work in progress. | |||
|
Thu, 09/05 13:00 |
Sigrid Kallblad |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
|
Thu, 02/05 13:00 |
Mathematical Finance Internal Seminar |
||
|
Thu, 25/04 13:00 |
Mathematical Finance Internal Seminar |
||
|
Thu, 28/02 13:00 |
Gechun Liang (Mathematics (Oxford)) |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| In this talk, We show that both reflected BSDE and its associated penalized BSDE admit both optimal stopping representation and optimal control representation. We also show that both multidimensional reflected BSDE and its associated multidimensional penalized BSDE admit optimal switching representation. The corresponding optimal stopping problems for penalized BSDE have the feature that one is only allowed to stop at Poisson arrival times. | |||
|
Thu, 21/02 13:00 |
Raphael Hauser (Mathematics (Oxford)) |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| 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, 14/02 13:00 |
Marek Musiela (Mathematics (Oxford)) |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| 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, 07/02 13:00 |
Vladimir Cherny (Mathematics (Oxford)) |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| 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, 31/01 13:00 |
Hanqing Jin (Mathematics (Oxford)) |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| 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, 24/01 13:00 |
Rasmus Varneskov (Oxford Man Institute) |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
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  -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,  . 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, 17/01 13:00 |
Mathematical Finance Internal Seminar |
||
|
No Seminar this week |
|||
|
Thu, 29/11/2012 13:00 |
Martin Klimmek |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| 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, 22/11/2012 13:00 |
Jeff Dewynn |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| 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, 08/11/2012 13:00 |
Doyne Farmer |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| 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, 01/11/2012 13:00 |
Various |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
|
Thu, 25/10/2012 13:00 |
Angel Ramos |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
|
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, 18/10/2012 13:00 |
Tigran Atoyan, Sean Ledger, Peter Spoida |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
|
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. ————— 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. —————— 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, 14/06/2012 13:00 |
Ian Angus |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
|
Thu, 07/06/2012 13:00 |
Radek Erban |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| 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, 24/05/2012 13:00 |
N/A |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
