abstracts

• Dr Ralph Bilger, d-fine

Valuation of American-Asian Options with the Longstaff-Schwartz Algorithm
The Least-Squares Monte Carlo (LSM) algorithm of Longstaff & Schwartz is a new and powerful approach for the valuation of the price of American options. This approach can also be applied to exotic, path-dependent options where the payoff and the value of the option depends on the value of the underlying, averaged over a given time-window (Asian options). So far, only American-Asian options have been considered where the starting point of the time window used for averaging is fixed. American-Asian options with rolling time-window, i.e. a time window of constant width are particularly complex since they constitute a non-Markovian problem, that can not be transformed to a problem with a finite number of state variables. In this work, the LSM algorithm is applied to American-Asian options with rolling time window. The value of the option is determined. The convergence of the algorithm is studied in dependence of the maximum degree of the polynomials used in the regression and the number of base variables.
[slides]

• Dr Andreas Binder, MathConsult, Linz

Accuracy does matter: High-End Numerical Techniques for the Robust Pricing of Structured Financial Instruments
Many partial differential equations which arise in pricing of financial instruments under, say, short rate models, are, to speak in the language of engineers, reaction-convection-diffusion equations. In the one-dimensional case, it turns out that combining symbolic techniques (Greens?s functions) and high order numerical integrations schemes delivers very accurate results also in cases where binomial trees fail. In the higher dimensional case, computational fluid dynamics has proven that finite element methods combined with streamline diffusion techniques are robust schemes for the treatment of these equations. We present the ideas behind these advanced numerical techniques.
Parameter calibration in interest rate models is a notorious instable problem. We present the reason behind this phenomenon, and how regularization techniques should be applied to stabilize the problem. This is joint work with MathConsult?s Computational Finance Group. Part of the work has been supported by the Austrian Science Foundation (Project E67: "Fast Numerical Methods for Computational Finance").
[paper]

• Dr Damir Filipovic, ETH Zurich

Swiss solvency test for insurers
I present and discuss the principles of the Swiss solvency test for insurers with regard to Solvency II.
[slides]

• Dr Marcus Fleck, Dresdner Bank

New Methods for measuring counterparty exposure consistent with Basel II Capital Accord
The Basel Committee acknowledged only recently that trading book issues have not been given sufficient attention over the past five years, and that the Committee had taken too conservative approach to counterparty risk of derivatives and repo-styled transactions. The stochastic nature of the default process combined with volatility in derivatives prices is a challenge not only for supervisiors but also for banking industry. Based on results from Monte Carlo Simulations we present new methods for measuring counterparty risk consistent with the Basel II framework. A fruitfull dialogue between industry representatives and the Basel Committee on those results has started already.
[slides]

• Dr Jürgen Hakala, Commerzbank

Higher order methods and non-uniform grid discretization in finite difference schemes for exotic option pricing

[slides]

• Prof Dieter Hess, HfB, Frankfurt

Does Information Quality Explain Asymmetric Price Reactions
It is well documented that the unanticipated news in the U.S. employment report trigger strong price reactions in bond markets around the world. Bayesian updating suggests that the quality of information, i.e. its precision, acts as a catalyst in determining the strength of the price reaction to a given piece of unanticipated information. However, it is difficult to test for this catalyzing effect due to a lack of precision data. Employing additional detail information, we extract release-specific precision measures. Based of these precision proxies, we show that prices respond significantly stronger to more precise information, even after controlling for an asymmetric price response to 'good' and 'bad' news.
This is joint work with Nikolaus Hautsch.
[paper], [slides]

• Dr Peter Neu, Dresdner Bank

Statistical Mechanics of Financial Markets and Applications in Risk Management
An overview is given how concepts from statistical physics of disorder systems like scaling, universality, criticality, and bubble nucleation can be used to explain so called "stylized" facts of financial time series. Such facts, which cannot be explained by the in banking popular log-normal diffusion model, are, e.g.,: Pareto distributed stock returns, long-ranged temporal volatility correlations (vs. short-ranged temporal stock return correlations), or negative return-volatility correlations. Besides the importance for market risk management it is shown how the dynamics underlying such phenomena is important for stress testing and capital allocation to credit risk and operational risk.
[paper], [paper], [slides]

• Dr Thorsten Oest, d-fine

A New Approach To Option Pricing For Discrete Hedging And Non-Gaussian Processes
The Black-Scholes option pricing method is correct under certain assumptions, among others continuous hedging and a log-normal underlying process. If any of these two assumptions is not fulfilled, a risk-less replication of an option is in general not possible.
To handle this case, a new pricing method is proposed. In contrast to other methods, not the risk of a hedging portfolio, but the option price is minimized. For the option price minimization the ratio of the averaged return to the averaged risk of the hedging portfolio is fixed. This resulting hedging procedure makes the option most competitive on the market.
A case study for realistic European plain vanilla and binary options was done. Compared to other methods, the option price is up to 10 % lower. In the continuous time limit for a log-normal process, the result of the method converges towards the Black-Scholes result.
[MSc Thesis], [slides]

• Dr Alex Popovici, Bonn University

Numerical analysis of extended Black-Scholes models
The multidimensional Black-Scholes model has been used as a basic and very effective tool for the valuation of derivative instruments in financial markets. In the last years empirical observations from the market (excess kurtosis, fat tails, smile and skew patterns of volatility surfaces, structural dependency between assets) hinted to the fact that the classical Black-Scholes framework is too restrictive for an accurate modelling of multidimensional financial markets. An extension of the Black-Scholes model focusing on the interdependency structure of assets and which delivers excellent result for pricing and hedging multi-asset financial derivatives was introduced by Albeverio and Steblovskaya in 2002. The aim of the talk is to present a numerical implementation of this model (historical estimation vs. calibration of parameters, pricing methods) and practical results obtained using market data (exotic options on baskets, volatility surfaces, etc). The advantages and drawbacks of this model will be discussed.
[paper], [slides]

• Prof LCG Rogers, University of Cambridge

Modelling liquidity and its effects
Liquidity is an important effect in the markets, yet it is hard to come up with a good definition, which not only has some economic explanation but also retains a reasonable degree of tractability. In this paper, we propose a simple microeconomic model in discrete time which carries over to the continuous-time setting; this results in a modification of the usual dynamics of portfolio wealth, which appears to be impossible to analyse exactly, though some asymptotic analysis can be carried through.
[slides]

• Prof Wolfgang Schmidt, HfB, Frankfurt

Hedging Basket Credit Derivatives with CDS
We investigate the pricing of basket credit derivatives and their hedging with single name credit default swaps (CDS). The market in credit default swaps quotes fair insurance premiums (spreads) whose dynamics is the natural starting point of our model. Pricing basket credit derivatives requires a model for the dependencies between the default times. In case of a pure jump filtration, dependencies are characterized by default implied spread changes. In this setup we derive a simple system of integral equations involving the notional amounts of the dynamic hedge positions, the price and the spread of a basket derivative. We provide some numerical examples of explicit hedging strategies and valuations of first-to-default baskets illustrating the approach.
[slides]

• Prof Robert G Tompkins, HfB, Frankfurt

Unconditional Return Disturbances: a Non Parametric Simulation Approach
Simulation methods are extensively used in Asset Pricing and Risk Management. The most popular of these simulation approaches, the Monte Carlo, requires model selection and parameter estimation. In addition, these approaches can be extremely computer intensive. Historical simulation has been proposed as a non-parametric alternative to Monte Carlo. This approach is limited to the historical data available.
In this paper, we propose an alternative historical simulation approach. Given a historical set of data, we define a set of standardized disturbances and we generate alternative price paths by perturbing the first two moments of the original path or by reshuffling the disturbances. This approach is totally non parametric when constant volatility is assumed, or semi-parametric in presence of GARCH (1,1) volatility and is shown without a loss in accuracy to be much more powerful in terms of computer efficiency than the Monte Carlo approach. This approach is extremely simple to implement and is shown to be an effective tool for the valuation of financial assets.
We apply this approach to simulate pay off values of options on the S&P 500 stock index for the period 1982-2003. To verify that this technique works, the common back-testing approach was used. The estimated values are insignificantly different from the actual S&P 500 options payoff values for the observed period.
This is joint work with Rita L. D'Ecclesia.
JEL classifications: C15, G13, G19
Keywords: Simulation Methods, Historical Simulation, Stochastic Volatility, Back-testing.
[paper], [slides]

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