Quantitative Finance

Participating researchers:

Michel BEINE

Antonio COSMA

Virginie TERRAZA

Georges HÜBNER

Since the middle of the 1980s, empirical finance has been shifting rapidly, and this shift is directly linked to the widening use of quantitative methods. Such a change is mostly due to the appearance of new financial assets, the improvement of empirical techniques in this field and the development of new databases, which rely – depending on the individual case – on infra-day variables, individual data, longer and longer time series, and/or non-stationary time series. Such an evolution requires research investigations both in fundamental econometrics and in empirical analysis. Quantitative finance deals with the testing of financial theories using financial databases, the estimation of variables, the measurement of asset prices and/or movements observed on the financial markets, and an empirical understanding of financial decision-making. Such analysis requires the development of new econometric protocols related to financial issues.

Time Series Analysis

In the last two decades there has been a dramatic change in the conceptual treatment of economic and financial time series. The modeling of such time series has moved from a static set-up to one that recognizes the importance of fitting together the time-varying features of macro-economic and of financial data. Possibly the most influential piece of work in financial econometrics of these last two decades, the ARCH model introduced by Engle in 1982 postulates that the main time-varying feature of a stationary series of returns is the conditional covariance structure of returns (often referred to as volatility ). The study of time-varying correlations has had an enormous impact on both theoretical and applied research in finance. This interest is explained by the close relationship between risk and expected return in asset pricing and by the central role played in risk management by measures of risk related to the volatility of a portfolio of assets. Indeed, the Basel 2 Accord on market risk indicates the minimum amount of capital required to cover the risk exposure of a financial institution. This amount is known as Value at Risk (VaR). Standard estimation techniques of VaR rely heavily on econometric tools based on the ARCH modeling philosophy. For instance, the Riskmetrics method, developed by JP Morgan in 1994, has become a reference for VaR estimation. Though the ARCH modeling approach has represented a major breakthrough in underlining the importance of second moments of time series, this approach is not always able to model satisfactorily all the stylized facts of financial time series.

Both academic researchers and practitioners are interested in new methodologies that allow for an improved description of the variability of financial time series. LSF researchers participate in this this effort by developing new econometric tools and by testing their performance on real data. One line of research is to depart from the parametric assumption of the ARCH family and to use a more flexible, semi-parametric or non-parametric, approach. To this end, new non-parametric estimators able to adapt to the peculiar characteristics of the new available databases (high frequency, irregularly spaced data) are being developed. Another line of research is to build estimators of risk measure that do not make use of a preliminary estimation of the volatility of the time series. Quantile regression, for instance, is a technique allowing building prediction intervals that can be used as a measure of risk. Risk estimation via the Gini decomposition is an alternative. One can obtain a new ratio of financial risk in the context of portfolio theory with less restrictive hypotheses on the distributions. The covariance matrix can be further decomposed using the Shapley Value. This new decomposition of between-risk measures provides suitable new trading risk indexes. These yield interesting information with which to classify securities according to different degrees of risk.

Market Microstructure Models

A deep understanding of the functioning of financial markets is a crucial issue both for participants in the financial market and for regulators willing to promote efficiency in the exchange. This need has originated a relatively recent but fast growing scientific literature trying to address crucial issues such as which particular trading mechanism is superior to another with respect to the efficiency of the market, or which institutional setting is to be adopted. A key issue in understanding the performance of financial markets is whether it respects the theoretical assumptions for efficient markets, such as for instance:

- the frictionless hypothesis , which translates in the financial language as the capacity of the market to provide liquidity at competitive trading costs;

- the absence of private information : analyzing the differences in the flow of distinct components of the market, such as the buy and sell orders on the same stock, can identify private information relating to a participant in the market.

Within this framework, one project of the LSF is to carry out a frequency domain analysis of co-movements in order-driven markets using high
frequency
data. The goal of this empirical analysis is to understand whether the arrival of new information is pervasive across all components of the market system. By aggregating at different horizons (frequencies) all the transaction data recorded in a financial marketplace it is possible to understand the speed at which one component of the market (e.g. the arrival process of buy orders) reacts to a change in the dynamics of another component of the market (e.g. the arrival process of sell orders). This kind of empirical analysis aims at providing the regulators with a tool able to assess the efficiency of the electronic order-driven markets, the trading mechanism chosen by most of the electronic marketplaces in Europe.

Asset Pricing Models

One particular field, which may be favored, is the estimation of asset pricing models in general and of news models in particular. The estimation of news models allows the identification of the specific news variables that tend to impact the price and the return of specific financial assets such as exchange rates or stock prices. A good illustration of this type of model is provided by Andersen, Bollerslev, Diebold and Vega (2002) (NBER WP 8959) for exchange rates. Importantly, since the estimation of this type of model is carried out at (very) high frequencies (daily, intra-daily…), one has to pay attention to particular statistical features of the data. These features concern time-varying volatilities, regime changes or intra-daily seasonality in the volatility process. Failure to account for these features would result in poor estimates of the parameters of these models and hence would give rise to inadequate conclusions. This calls for the development of estimation techniques that could deal with these features.

Another classic research line in asset pricing is derivative pricing using continuous time finance tools. A deep understanding of these pricing techniques is crucial in structuring and correctly pricing complex products such as credit derivatives, which are one of the major tools used by banks to diversify and distribute their credit risk. One research project of the LSF aims at developing fast numerical algorithms able to price complex derivatives. In particular, the goal is to build a very general numerical pricing technique to be used for a large class of asset dynamics with jump component and stochastic volatility.

LSF working papers related to this research axis