We estimate a general microstructure model of the transitory and permanent impact of order flow on stock prices. Jumps are detected in both the transaction price (observation equation) and fundamental value (state equation). The model’s parameters and variances are updated in real time. Prices can be altered by both the size and direction of trades, and the effects of buy-initiated and sell-initiated trades are different. We estimate this model using tick-by-tick data for 12 large-capitalization stocks traded on the Euronext-Paris Bourse. We find that, at tick frequency, the overnight return, the intraday jumps, and the continuous innovations represent approximately 7%,8.5%, and 36.7% of the total variation of stock returns. The microstructure model explains on average 47.7% of the total variation. Once jumps are filtered and parameters are estimated in real time, we also find that the price impact of trades is symmetric on average. However, the price of highly liquid stocks with a large proportion of sell-initiated orders tends to be more sensitive to buy trades, whereas the price of less liquid stocks with a large proportion of buy-initiated orders tends to be more sensitive to sell trades.

In this paper, we compare various methods that extract a Risk Neutral Density (RND) out of PIBOR interest-rate futures options and we investigate how traders react to a political event. Our benchmark model derives from A. Brace, D. Ga̧tarek, M. Musiela [Mathematical Finance 7 (1997) 127–155]. We also consider a mixture of log-normals (as in W.R. Melik, C.P. Thomas, Journal of Financial and Quantitative Analysis 32 (1997) 91–116), an Hermite expansion (as in P. Abken, D.B. Madan, S. Ramamurtie, Estimation of risk-neutral and statistical densities by Hermite polynomial approximation: with an application to Eurodollar Futures Options, Federal Reserve Bank of Atlanta, 1996), and a method based on Maximum Entropy (according to P. Buchen, M. Kelly, Journal of Financial and Quantitative Analysis 31 (1996) 143–159). We take care of the early exercise feature and we show how to approximate RNDs for a fixed time to maturity. The various methods generate similar RNDs. A daily panel of options running from February 1997 to July 1997 reveals that operators expected the snap election a few days before the official announcement was made and that a substantial amount of political uncertainty subsisted even a month after the elections. Uncertainty evolved with polls forecasts of the future government.

WE WARN OF A CLASS of problems that can occur when inverting confluent characteristic functions (CF's). The term confluence is often used in Mathematics in connection with analysis and/or dynamic (difference, differential, and integral) equations; for example, see the classic text by Whittaker and Watson (1927). A confluence (of singularities) is a joint degeneracy that occurs within a function; here, the CF. When one is dealing with the CF of a k-dimensional variate where k > 1, these joint degeneracies can distort the derivation of the marginal density of some lower-dimensional combination of the k components. The distortions are both analytical and numerical. In this note, we first express the distributional problem in the simplest bivariate case, then clarify it with examples from a simple autoregressive (AR) model. Let R, S be two continuous (for simplicity) variates based on a sample of n observations, with joint CF pn(u,v) =E[euR+ivS], i = , and Pr{S > 0} = 1. The joint density h,jr, s) of R and S is expressed by means of the inversion formula as

This article presents a general framework for identifying and modeling the joint-tail distribution based on multivariate extreme value theories. We argue that the multivariate approach is the most efficient and effective way to study extreme events such as systemic risk and crisis. We show, using returns on five major stock indices, that the use of traditional dependence measures could lead to inaccurate portfolio risk assessment. We explain how the framework proposed here could be exploited in a number of finance applications such as portfolio selection, risk management, Sharpe ratio targeting, hedging, option valuation, and credit risk analysis.