The paper contains a phenomenological description of the whole US forward rate curve (FRC), based on data in the period 1990-1996. It is found that the average deviation of the FRC from the spot rate grows as the square-root of the maturity, with a prefactor which is comparable to the spot rate...

We explore the precise link between option prices in exponential Lévy models and the related partial integro-differential equations (PIDEs) in the case of European options and options with single or double barriers. We first discuss the conditions under which options prices are classical...

This paper contains a statistical description of the whole U.S. forward rate curve (FRC), based on data from the period 1990-1996. We find that the average deviation of the FRC from the spot rate grows as the square- root of the maturity, with a proportionality constant which is comparable to...

To execute a trade, participants in electronic equity markets may choose to submit limit orders or market orders across various exchanges where a stock is traded. This decision is influenced by the characteristics of the order flow and queue sizes in each limit order book, as well as the...

To execute a trade, participants in electronic equity markets may choose to submit limit orders or market orders across various exchanges where a stock is traded. This decision is influenced by the characteristics of the order flow and queue sizes in each limit order book, as well as the...

We study the short-time asymptotics of conditional expectations of smooth and non-smooth functions of a (discontinuous) Ito semimartingale; we compute the leading term in the asymptotics in terms of the local characteristics of the semimartingale. We derive in particular the asymptotic behavior...

We study the price impact of order book events--limit orders, market orders, and cancellations--using the NYSE Trades and Quotes data for fifty U.S. stocks. We show that, over short time intervals, price changes are mainly driven by the order flow imbalance (OFI), defined as the imbalance...

We propose a tractable framework for quantifying the impact of fire sales on the volatility and correlations of asset returns in a multi-asset setting. Our results enable to quantify the impact of fire sales on the covariance structure of asset returns and provide a quantitative explanation for...

type="main" xml:lang="en" <p>We propose a market–based approach to the modelling of implied volatility, in which the implied volatility surface is directly used as the state variable to describe the joint evolution of market prices of options and their underlying asset. We model the evolution of...</p>

Benoit Mandelbrot, mathématicien et savant multidisciplinaire, s'intéressa très tôt dans sa carrière à l'étude statistique des données économiques et financières et fut à l'origine de nombreuses idées importantes dans la modélisation statistique des risques financiers, sujet qui le...