Christian Menn
Karlsruhe Institute of Technology
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Publication
Featured researches published by Christian Menn.
Mathematical Methods of Operations Research | 2009
Christian Menn; Svetlozar T. Rachev
Although asset return distributions are known to be conditionally leptokurtic, this fact has rarely been addressed in the recent GARCH model literature. For this reason, we introduce the class of smoothly truncated stable distributions (STS distributions) and derive a generalized GARCH option pricing framework based on non-Gaussian innovations. Our empirical results show that (1) the model’s performance in the objective as well as the risk-neutral world is substantially improved by allowing for non-Gaussian innovations and (2) the model’s best option pricing performance is achieved with a new estimation approach where all model parameters are obtained from time-series information whereas the market price of risk and the spot variance are inverted from market prices of options.
Computational Statistics & Data Analysis | 2006
Christian Menn; Svetlozar T. Rachev
An algorithm for the approximation of @a-stable densities is developed and compared with similar approximation methodologies. The proposed approach employs an adaptive Simpson rule for the quadrature of the Fourier inversion integral and asymptotic Bergstrom series expansions for the tails of the density. It is guaranteed that the approximation integrates precisely to unity which is helpful for numerical maximum-likelihood routines. The accuracy of the algorithm has been verified with respect to the values obtained by Nolans program STABLE for a grid of parameter values. It is shown that a significant reduction of the computational effort with respect to Nolans program can be achieved while maintaining a satisfying accuracy.
European Journal of Operational Research | 2005
Christian Menn; Svetlozar T. Rachev
We develop an option pricing model which is based on a GARCH asset return process with α-stable innovations with truncated tails. The approach utilizes a canonic martingale measure as pricing measure which provides the possibility of a model calibration to market prices. The GARCH-stable option pricing model allows the explanation of some well-known anomalies in empirical data as volatility clustering and heavy tailedness of the return distribution. Finally, the results of Monte Carlo simulations concerning the option price and the implied volatility with respect to different strike and maturity levels are presented.
Archive | 2006
Svetlozar T. Rachev; Anna Chernobai; Christian Menn
Until very recently, it has been believed that banks are exposed to two main types of risks: credit risk (the counterparty failure risk) and market risk (the risk of loss due to changes in market indicators, such as interest rates and exchange rates), in the order of importance. The remaining financial risks have been put in the category of other risks, operational risk being one of them. Recent developments in the financial industry have shown that the importance of operational risk has been largely under-estimated. Newly defined capital requirements set by the Basel Committee for Banking Supervision in 2004, require financial institutions to estimate the capital charge to cover their operational losses [6].
Archive | 2010
Anna Chernobai; Christian Menn; Svetlozar T. Rachev; Stefan Trück
The recently finalized Basel II Capital Accord requires banks to adopt a procedure to estimate the operational risk capital charge. Under the Advanced Measurement Approaches, that are currently mandated for all large internationally active US banks, require the use of historic operational loss data. Operational loss databases are typically subject to a minimum recording threshold of roughly
Archive | 2005
Svetlozar T. Rachev; Christian Menn; Frank J. Fabozzi
10,000. We demonstrate that ignoring such thresholds leads to biases in corresponding parameter estimates when the threshold is ignored. Using publicly available operational loss data, we analyze the effects of model misspecification on resulting expected loss, Value-at-Risk, and Conditional Value-at-Risk figures and show that underestimation of the regulatory capital is a consequence of such model error. The choice of an adequate loss distribution is conducted via in-sample goodness-of-fit procedures and backtesting, using both classical and robust methodologies.
Journal of Banking and Finance | 2007
Michael Bierbrauer; Christian Menn; Svetlozar T. Rachev; Stefan Trück
Archive | 2005
Anna Chernobai; Christian Menn; Stefan Trück; Svetlozar T. Rachev
Archive | 2005
Svetlozar T. Rachev; Christian Menn; Frank J. Fabozzi
Archive | 2006
Svetlozar T. Rachev; Christian Menn