Statistics and Operations Research Seminars 2011--2012, Department of Economics and Business, Pompeu Fabra University

• Thursday, September 22, 17:00, room 20.137.
  Frank van der Meulen (Delft University of Technology)
  Bayesian estimation of the drift of a diffusion process.
  Abstract. In this talk I will consider estimating the drift function of a continuously observed diffusion process. The Bayesian approach entails the specification of a prior distribution on the drift function. I will first discuss a result that gives sufficient conditions for obtaining convergence rates for the posterior distribution. These conditions depend both on the prior and the size of the model. From a more practical perspective, I will introduce a reversible jump MCMC algorithm to obtain draws form the posterior distribution in case of a series prior using an expansion of the drift in a hierarchical basis. If time permits, I will discuss consistency of the prior and computational issues in case of discrete time observations. This concerns joint work with Moritz Schauer (TU Delft), Aad van deer Vaart (VU Amsterdam) and Harry van Zanten (TU Eindhoven).

  
  

• Tuesday, December 13, 12:00, room 20.287.
  Javier Vicente (UPF)
  High-Frequency Finance: A Complexity Science Approach.
  Abstract. High‐Frequency Finance is a new coined term that it is related to the raise of modern electronic markets where trades and quotes happen in very short time intervals: seconds, or even shorter. All the information about trades, quotes, e.g., broker, time stamp, price, size, etc. is recorded in daily datasets which bring great opportunities of researching a complex system given the huge amount of accurate data. I will present two problems. The first one is a classical problem in Finance: the shape and evolution of the pdf of returns. Several attempts have tried to explain empirical return distribution, but in general all these previous explanations failed in reproducing the tails of the empirical distribution. Here, based on a theory – Superstatistics – developed for understanding critical phenomena in Mechanical Statistics I have been able to explain the pdf and its temporal evolution. The second problem is about optimal execution of large orders that must be split into smaller ones to avoid the huge market price impact they would cause in case of being executed in one only transaction. In this case, I am interested on the trades of every single market participant instead of on the aggregate of all of them. I study two different markets: LSE, and SSE. Being in both cases the empirical results compatible with a simple economic law related to optimal execution; independently of the specific features of each market.