Statistics meets Finance
This workshop is intended to give a platform for researchers from Statistics and Finance to meet and exchange ideas. It will take place on the 3rd of September 2009 at Technical University of Chemnitz. Participation is free of charge. The detailed time-schedule will follow soon.
The detailed programm is here
We will have the following lectures:
Statistical Analysis of Self-Exciting Processes with Applications to Marketing
We present a statistical analysis of so-called self-exciting processes. These processes are driven by compensators incorporating both internal and external history, thus allowing for complicated but realistic dynamics. An application to the purchasing behavior of customers and the impact of TV-promotion is studied in detail.
Credit risk and incomplete information: filtering and EM parameter estimation
We consider a reduced-form credit risk model where default intensities and interest rate are functions of a not fully observable Markovian factor process, thereby introducing an information-driven default contagion effect among defaults of different issuers. We determine arbitrage-free prices of OTC products coherently with information from the financial market, in particular yields and credit spreads and this can be accomplished via a filtering approach coupled with an EM-algorithm for parameter estimation.
Stochastic processes with structural breaks
A new approach to LIBOR modelling
We provide a general and flexible approach to LIBOR modeling based on the class of affine factor processes. Our approach respects the basic economic requirement that LIBOR rates are non-negative, and the basic requirement from mathematical finance that LIBOR rates are analytically tractable martingales with respect to their own forward measure. Additionally, and most importantly, our approach also leads to analytically tractable expressions of multi-LIBOR payoffs. This approach unifies therefore the advantages of well-known forward price models with those of classical LIBOR rate models. Several examples are added and prototypical volatility smiles are shown. We believe that the CIR-process based LIBOR model might be of particular interest for applications, since closed form valuation formulas for caps and swaptions are derived.
Semismooth Newton Methods for Portfolio Optimization
We are considering a continuous-time market model of one bank account and one stock. Trading the stock incurs transaction costs proportional to the trading volume. Given the interest rate, the stock trend parameter, the transaction costs and the volatility, the values X_0 and X_1 of the bank account and the stock, respectively, evolve according to a certain stochastic differential equation. The objective is to maximize the expected power-law utility of the total wealth at a given terminal time T. Admissible trading strategies ensure positive total wealth at all times. The associated value function satisfies a Hamilton-Jacobi-Bellman equation subject to terminal and boundary conditions. In the presentation, we address semismooth Newton methods which allow for the efficient numerical solution and give some examples.
Conditional beta pricing models: A nonparametric approach
This work proposes a two-stage procedure to estimate conditional beta pricing models that allows for flexibility in the dynamics of assets' covariances with risk factors and market prices of risk (MPR). First, conditional covariances are estimated nonparametrically for each asset and period using the time-series of previous data. Then, time-varying MPR are estimated from the cross-section of returns and covariances using the entire sample. The consistency and asymptotic normality of the estimators is proved. An empirical application of the method to the term structure of interest rates highlights the drawbacks of existing parametric models.
Statistical aspects of risk comparison
Suppose that the random variables X and Y represent the loss associated with two insurance policies or other financial contracts. The comparison of the associated risks is usually based on the distributions of X and Y, which requires some partial order on the set of distribution functions.
We introduce and discuss various tests for hypotheses concerning the stop-loss order, a popular choice in insurance mathematics.
The talk is based on joint work with L. Baringhaus.