WEDNESDAY 14 OCTOBER 2009
Damien Lamberton (Marne-La-Vallée)
Title: On the approximation of the supremum of a Lévy process
Abstract: This talk is based on joint work with El Hadj Aly Dia. After some remarks on the distribution of the supremum of a Lévy process, we will present some estimates for the difference between the supremum of a Lévy process and its discrete maximum. We will also discuss the truncation of small jumps. This study is motivated by lookback and barrier options in exponential Lévy models.
WEDNESDA Y 21 OCTOBER 2009
Goran Peskir (Manchester)
Title: Selling a Stock at the Ultimate Maximum
Abstract: I will review recent results on the problem of predicting the maximum when the stock price follows a geometric Brownian motion.
WEDNESDAY 28 OCTOBER 2009
Paul Schneider (Warwick)
Title: Estimation of Nonlinear Diffusion Processes and Applications in Finance
Abstract: We introduce a simple but general continuous-time asset pricing framework that combines semi-analytic pricing with a wealth of flexibility in time-series modelling. Our framework guarantees the existence of the processes used and gives a justification -- for empirical purposes -- to work with nonlinear specifications not considered in the literature so far. Additional flexibility turns out to be econometrically relevant: a nonlinear stochastic volatility diffusion model for the joint time-series of the S&P 100 and the VXO implied volatility index data shows superior forecasting power over standard specifications for implied--, and realized variance forecasting. Joint work with A. Mijatovic.
WEDNESDAY 4 NOVEMBER 2009
James Gleeson (Limerick)
Title: Cascades on random networks
Abstract: Network models may be applied to many complex systems, e.g. the Internet, the World Wide Web, inter-bank lending networks, etc. Cascade dynamics can occur when the (binary) state of a node is affected by the states of its neighbours in the network. Such models have been used to aid understanding of the spread of cultural fads and the diffusion of innovations, and can be generalized to include percolation problems, k-core sizes, and disease spread on networks. For this class of problems, I present recent results on the analytic determination of the expected size of cascades on networks of arbitrary degree distribution, and outline some extensions of this research. Application to models of contagion and systemic risk within banking networks will also be discussed (joint work with Sébastien Lleo and Tom Hurd).
TUESDAY 10 NOVEMBER 2009
Umut Cetin (LSE)
Title: Dynamic Markov bridges motivated by models of insider trading
Abstract: Given a Markovian Brownian martingale Z, we build a process X which is a martingale in its own filtration and satisfies X(1) = Z(1). We call X a dynamic bridge, because its terminal value Z(1) is not known in advance. We compute explicitly its semimartingale decomposition under both its own filtration and the filtration generated jointly by X and Z. Our construction is heavily based on parabolic PDE's and filtering techniques. As an application, we explicitly solve an equilibrium model with insider trading, that can be viewed as a non-Gaussian generalization of Back and Pedersen, where insider's additional information evolves over time (joint work with L. Campi and A. Danilova).
WEDNESDAY 25 NOVEMBER 2009
Jose Da Fonseca (Auckland)
Title: Riding on the Smiles
Abstract: This paper investigates the calibration performance of several multifactor stochastic volatility models. There is an empirical evidence that the dynamics of the implied volatility surface is driven by several factors. This leads to the extensions of the seminal Heston stochastic volatility model. Using a data set of derivatives on the major indices we study the calibration properties of these models using the FFT as the pricing methodology. We also study if adding jumps improves significantly the calibration accuracy of the models. We explain the advantages of the Wishart based stochastic volatility model when dealing with stochastic correlation risk. Then we focus on basket option pricing models and more precisely on the WASC model (Wishart Affine Stochastic Correlation) proposed by [Da Fonseca, Grasselli and Tebaldi, 2007]. We analyse the calibration property of this model and compare it with another model based on the Heston model. Finally, we provide some price approximations for vanilla options in the spirit of [Benabid, Bensusan and El Karoui, 2009] that are very useful to speed up the pricing process thus leading to reasonable calibration time. Also we provide some results on Malliavin calculus that allow for efficient computation of the sensitivities for derivative products in our models.
TUESDAY 1 DECEMBER 2009
Peter Carr (NYU & Bloomberg)
Title: What does an option price mean?
Abstract: It is well known that the market price of a standard option reflects the risk-neutral mean of its path-independent payoff. It is less well known that this same option price also reflects the risk-neutral mean of various path-dependent payoffs. We give several examples of such payoffs which together suggest that option prices convey much more information than one might initially expect.
WEDNESDAY 9 DECEMBER 2009
Vlad Bally (Marne-la-Vallée)
Title: Tube estimates for Itô processes and applications to stochastic volatility models
Abstract: We give lower bounds for the probability that an Itô process stays in a tube around a deterministic curve up to the time T. This in particular gives lower bounds for arriving in a ball around a specific point in the state-space at time T. We apply these estimates to a wide class of stochastic volatility models with local (i.e. non-constant) coefficients. Such models have become very common in financial markets because they are capable of calibrating perfectly to the implied volatility surface while retaining the desired dynamics of the spot process. We also prove that the moments of the stock in such a model can blow up in finite time (this is already known for the classical Heston model with constant coefficients). Finally we give estimates for the density of the law of the stock.