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Empirical properties of asset returns: stylized facts and statistical issues
We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to allExpand
Financial Modelling with Jump Processes
WINNER of a Riskbook.com Best of 2004 Book Award!During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much hasExpand
Model Uncertainty and its Impact on the Pricing of Derivative Instruments
Uncertainty on the choice of an option pricing model can lead to "model risk" in the valuation of portfolios of options. After discussing some properties which a quantitative measure of modelExpand
A Stochastic Model for Order Book Dynamics
A continuous-time stochastic model that can effectively capture the short-term dynamics of a limit order book and evaluate the performance of a simple trading strategy based on the results is proposed. Expand
Robustness and Sensitivity Analysis of Risk Measurement Procedures
Measuring the risk of a financial portfolio involves two steps: estimating the loss distribution of the portfolio from available observations and computing a ``risk measure" which summarizes the riskExpand
Functional Ito calculus and stochastic integral representation of martingales
We develop a non-anticipative calculus for functionals of a continuous semimartingale, using an extension of the Ito formula to path-dependent functionals which possess certain directionalExpand
Change of variable formulas for non-anticipative functionals on path space ✩
We derive a change of variable formula for non-anticipative functionals defined on the space of Rd-valued right-continuous paths with left limits. The functionals are only required to possess certainExpand
Measuring systemic risk
The role of systemic risk in the recent crisis and the failure of current risk measurement and management methods to cope with it bring under question some of the premises underlying traditionalExpand
A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models
An explicit-implicit finite difference scheme which can be used to price European and barrier options in option pricing theory when the random evolution of the underlying asset is driven by a Levy process or, more generally, a time-inhomogeneous jump-diffusion process is proposed. Expand
Network Structure and Systemic Risk in Banking Systems
We present a quantitative methodology for analyzing the potential for contagion and systemic risk in a network of interlinked financial institutions, using a metric for the systemic importance ofExpand