Bertrand Maillet

X-SOM and L-SOM: A double classification approach for missing value imputation

In this paper, a new method for the determination of missing values in temporal databases is presented. It is based on a robust version of a nonlinear classification algorithm called self-organizing maps and it consists of a combination of two classifications in order to take advantage of spatial as well as temporal dependencies of the dataset. This double classification leads to a significant improvement of the estimation of the missing values. An application of the missing value imputation for hedge fund returns is presented.

An index of market shocks based on multiscale analysis

Abstract Financial markets are places of sudden and violent price movements. Nevertheless, financial crises lack a universally recognized way of assessing their gravity. This has motivated the measure recently proposed and applied to the exchange rates market by Zumbach et al (2000a Int. J. Theor. Appl. Finance 3 347–55). This measure relies on an analogy with geophysics: the scale of market shocks (SMS) is equivalent to the Richter scale used for earthquakes. More precisely, as a market is the place where economic agents—with different investment horizons—interact, the SMS definition is a weighted aggregation of volatility measures corresponding to these different horizons. In this paper, we implement and apply a similar measure to stock markets, and adapt it to take into account some extra features of these markets. The volatilities are first described, and then used to assess the market instability perceived by a market participant. The evolution of our index of market shocks (IMS)—after rescaling for easy interpretation—is presented using different computational methods. The IMS is then compared with another multiscale measure, the multifractal spectrum width, and we also investigate the links between the IMS and the daily close-to-close returns and volatility. Finally, we describe the recent turbulence on the French market using the IMS as an exploratory tool, concluding that the events of September 2001 proved to be a major shock compared to the Russian and Asian crises. * Paper presented at Applications of Physics in Financial Analysis (APFA) 3, 5–7 December 2001, Museum of London, UK.

Further Insights on the Puzzle of Technical Analysis Profitability

This paper extends current results concerning technical analysis efficiency on the foreign exchange market and attempts to determine whether filtering the raw exchange rate series with some trading rule significantly changes its characteristics. Because of the non-normality of exchange rate series, bootstrap methods are used on the main daily exchange rates since 1974 to show technical analysis performance. The technical analysis strategy tested generates returns whose distribution is significantly different from the basic series. The robustness of the results is tested in and out-of-sample and an explanation of the technical analysis performance based on its filtering properties is suggested.

Understanding and reducing variability of SOM neighbourhood structure

The self-organizing map (SOM) is a nonlinear unsupervised method for vector quantization. In the context of classification and data analysis, the SOM technique highlights the neighbourhood structure between clusters. The correspondence between this clustering and the input proximity is called the topology preservation. We present here a stochastic method based on bootstrapping in order to increase the reliability of the induced neighbourhood structure. Considering the property of topology preservation, a local approach of variability (at an individual level) is preferred to a global one. The resulting (robust) map, called R-map, is more stable relatively to the choice of the sampling method and to the learning options of the SOM algorithm (initialization and order of data presentation). The method consists of selecting one map from a group of several solutions resulting from the same self-organizing map algorithm, but obtained with various inputs. The R-map can be thought of as the map, among the group of solutions, corresponding to the most common interpretation of the data set structure. The R-map is then the representative of a given SOM network, and the R-map ability to adjust the data structure indicates the relevance of the chosen network.

A note on skewness and kurtosis adjusted option pricing models under the Martingale restriction

Several authors have proposed series expansion methods to price options when the risk-neutral density is asymmetric and leptokurtic. Among these, Corrado and Su (1996) provide an intuitive pricing formula based on a Gram–Charlier Type A series expansion. However, their formula contains a typographic error that can be significant. Brown and Robinson (2002) correct their pricing formula and provide an example of economic significance under plausible market conditions. The purpose of this comment is to slightly modify their pricing formula to provide consistency with a martingale restriction. We also compare the sensitivities of option prices to shifts in skewness and kurtosis using parameter values from Corrado and Su (1996) and Brown and Robinson (2002), and market data from the French options market. We show that differences between the original, corrected and our modified versions of the Corrado and Su (1996) original model are minor on the whole sample, but could be economically significant in specific cases, namely for long maturity and far-from-the-money options when markets are turbulent.

The Approximate Option Pricing Model: Performances and Dynamic Properties

Using high frequency data from ParisBourse SA, this article examines pricing and hedging performances of the Jarrow and Rudd (Journal of Financial Economics 10 (1982) pp. 347–369) model. We first find that this model improves the pricing of CAC 40 index European call options whether in-sample or out-of-sample, and whatever economic or statistic criterion may be used. Moreover, simple models for implied moments lead—in a dynamic setting—to results very close to those from in-sample optimization. But, we also find that this model does not improve hedging strategy and that the Black and Scholes (Journal of Political Economy (1973) pp. 637–655) model is still difficult to beat.

Sparse Linear Combination of SOMs for Data Imputation: Application to Financial Database

This paper presents a new methodology for missing value imputation in a database. The methodology combines the outputs of several Self-Organizing Maps in order to obtain an accurate filling for the missing values. The maps are combined using MultiResponse Sparse Regression and the Hannan-Quinn Information Criterion. The new combination methodology removes the need for any lengthy cross-validation procedure, thus speeding up the computation significantly. Furthermore, the accuracy of the filling is improved, as demonstrated in the experiments.

Completing hedge fund missing net asset values using Kohonen maps and constrained randomization

Analysis of financial databases is sensitive to missing values (no reported information, provider errors, outlier filters...). Risk analysis and portfolio asset allocation require cylindrical and complete samples. Moreover, return distributions are characterised by non-normalities due to heteroskedasticity, leverage effects, volatility feedbacks and asymmetric local correlations. This makes completion algorithms very useful for portfolio management applications, specifically if they can deal properly with the empirical stylised facts of asset returns. Kohonen maps constitute powerful nonlinear financial classification tools (see [3], [4] or [6] for instance), following the approach of Cottrell et al. (2003), we use a Kohonen algorithm (see [2]), altogether with the Constrained Randomization Method (see [8]) to deal with mutual fund missing Net Asset Values. The accuracy of rebuilt NAV estimated series is then evaluated according to a comparison between the first moments of the series.

A R-SOM Analysis of the Link between Financial Market Conditions and a Systemic Risk Index Based on ICA-Factors of Systemic Risk Measures

Due to the recent financial crisis, several systemic risk measures have been proposed in the literature for quantifying financial system wide distress. In this note we propose an aggregated Index for financial systemic risk measurement based on EOF and ICA analyses on the several systemic risk measures released in the recent literature. We use this index to further identify the states of the market as suggested in Kouontchou et al. [18]. We show, by characterizing markets conditions with a robust Kohonen Self-Organizing Maps algorithm that this measure is directly linked to crises markets states and there is a strong link between return and systemic risk.

Increasing reliability of SOMs’ neighbourhood structure with a bootstrap process

One of the most interesting features of self-organizing maps is the neighbourhood structure between classes highlighted by this technique. The aim of this paper is to present a stochastic method based on bootstrap process for increasing the reliability of the induced neighbourhood structure. The robustness under interest here concerns the sensitivities of the output to the sampling method and to some of the learning options (the initialisation and the order of data presentation). The presented method consists in selecting one map between a group of several solutions resulting from the same self-organizing map algorithm but with various inputs. The selected (robust) map, called R-map, can be perceived as the map, among the group, that corresponds to the most common interpretation of the data set structure.