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Current CoFE Research Projects
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Prof. Dr. Jan Beran
Wavelet Analysis of Multivariate Financial Time Series
Abstract:
We consider multivariate time series with seasonal and a long-term component, together with wavelet-based estimation.
The main questions are:
a) optimal estimation of the components, and of the multivariate regression spectrum,
b) comparison of direct and indirect estimates of the regression spectrum,
c) prediction,
d) applications to high frequency data,
e) extensions to models with long-memory stochastic components.
Prof. Dr. Robert Denk
Numerics of Stochastic Differential Equations and Applications to Portfolio Management Models
Abstract:
This project analyses optimal stochastic control problems arising in the context of portfolio management models. As the main tool for solving such problems, backwards stochastic differential equations (BSDEs) and their numerical approximations will be chosen. BSDEs are connected to optimal control problems by the maximum principle. In the project, numerical approaches to BSDEs will be developed, discussed, and analysed. One of the central tasks here is the numerical computation of conditional expectations which appear in iteration methods to solve BSDEs.
In this project, first, the application of BSDEs to optimization problems for portfolio management problems is considered, and the question of the applicability of the maximum principle is investigated. Second, various iteration methods for solving BSDEs are compared and further developed. Here the focus lies on avoiding the nesting of conditional expectations. Finally, the project analyses numerical methods to compute conditional expectations. In particular, Monte-Carlo regression methods will be considered. The developed methods will be implemented in Matlab and/or C.
Prof. Dr. Dr. h.c. Günter Franke
Design and Trade of CDO Transactions
Abstract:
This project, first, looks at the design of CDO transactions. CDO transactions comprise CLO (Collateralized Loan Obligation) transactions and CBO (Collateralized Bond Obligation) transactions. Banks may be interested to securitize a debt portfolio because they want to reduce their default risk and/or to lower their refinancing costs. Information asymmetries play a major role in these transactions. Therefore, the project analyzes the relationship between the quality of the debt portfolio and some characteristics of the CDO transactions like the size of the first loss position, the choice between synthetic and true sale-transactions and the tranching of claims. Second, the project aims to derive an optimal design of these transactions by analyzing the effects of various credit enhancements. This is done by simulating the loss rate distributions of transactions for different designs and comparing the implications for banks. Third, the project looks into the pricing of CDO tranches. This is done by empirically analyzing the pricing kernels which govern the pricing of these tranches. This research is complemented by Cristian Chetran who analyses the design of mortgage-backed transactions.
Background Risks and Valuation of Financial Assets
Abstract:
This project analyzes how tradability of default risks affects the credit policy of banks and the valuation of loans. The typical loan given by a bank to a small or medium sized company is kept by the bank until maturity. The default risk then is a background risk. Background risks not only affect the bank´s taking of tradable risks but also the bank´s willingness to lend. If credit risks are tradable, then banks can sell part of these risks and thereby manage their risk. The theoretical part of the project analyses, first, a model with given interest rates of loans and asks how tradability of loans affects the bank´s loan policy in a multi period model. To make tradability useful, heterogeneity of banks is required. Hence, the project focuses on the interaction between the primary market based lending policy and secondary market based trading. Second, an equilibrium model will be analysed in which the interest rates of loans are endogenous. Third, the results derived in the theoretical analysis will be tested on European bank data.
Prof. Dr. Jens Jackwerth
Probability of Default and Optimal Control of Risk within a Firm
Abstract:
In this project we investigate the price and credit risks of firms where the manager has the ability to optimally control the risk taking of the firm given that he maximizes the utility of wealth derived from his compensation package. Such control has so far not been modeled in a structural model, and we are thus able to show for the first time the impact of such control on security prices and default patterns. We model firms more realistically since managers are paid in order to make exactly such choices concerning risk. Ideally, the choice of compensation will induce the manager to take risks in a utility maximizing way such that the risk taking coincides with the desired risk taking of the investors. Managerial control makes the firm´s value then follow a controlled stochastic process. The value of the firm´s securities (stocks, bonds and options) will naturally depend on the risk taking of the manager. We solve this problem in discrete time using an efficient numerical method. This has the advantage that we do not need to make simplifying assumptions on e.g. risk taking in order to get closed form solutions. Also, a discrete time set-up naturally generates larger default probabilities at short maturities since it is possible to bankrupt the firm even over short time intervals.
Prof. Dr. Ansgar Jüngel
Numerical Solution and Modeling of Nonlinear Partial Differential Equations for Credit and Price Risks
Abstract:
This project analyzes nonlinear effects occuring in the pricing of financial assets, numerically and analytically. In particular, we are concerned with Hamilton-Jacobi-Bellman equations and other nonlinear partial differential equations. The first project goal is the time-continuous modeling and numerical simulation of a portfolio with credit risks. In a second part we address the portfolio problem of a hedge fund manager who is paid an incentive fee additionally to a fixed premium. The third project goal encompasses the development of efficient numerical methods for solving infinite dimensional constrained optimization problems, as in the estimation of local volatility functions on options with multiple underlyings.
Prof. Dr. Winfried Pohlmeier
Multivariate Analysis of Market Risk and Trading Processes on the Transaction Level
Abstract:
The aim of this project is twofold. The first research focus is on measuring and forecasting multivariate market risks and their applications in finance. This is achieved by using high-frequency data released by many exchanges (e.g. NYSE) to construct precise estimates of the variance and covariance structure of the assets or markets under consideration. Considerable attention within this approach is devoted to the modeling of market microstructure effects as they are of key importance in shaping the statistical properties of high-frequency data. The second area of research within the project is the analysis of trading processes and traders´ behavior. To this end high-frequency data containing information on the trading history of individual investors is used. From econometric point of view models for marked point processes, duration- and intensity-based models are well suited to describe such datasets. This allows for dynamic modeling of multivariate processes (e.g. bid and ask prices, trading volumes) in order to comprehensively describe market liquidity and the dynamics of limit order books. The availability of individual trading histories enables testing of various behavioral finance hypotheses, among which is the so called disposition effect.
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