Modeling financial asset returns with shot noise processes

Modeling Financial Security Returns Using Lévy Processes

Lévy processes can capture the behaviors of return innovations on a full range of financial securities. Applying stochastic time changes to the Lévy processes randomizes the clock on which the processes run, thus generating stochastic volatilities and stochastic higher return moments. Therefore, with appropriate choices of Lévy processes and stochastic time changes, we can capture the return dy...

The News in Financial Asset Returns

Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W First Quarter 2004 A re returns on financial markets useful for predicting the future course of the economy? It is widely thought that financial markets’ movements reflect the economy’s future and that finding the message in financial asset returns is one way to discern this future. The message is not always clear, though. For example,...

Shot Noise Cox Processes

Catastrophe Insurance Modelled with Shot-noise Processes

Shot-noise processes generalize compound Poisson processes in the following way: a jump (the shot) is followed by a decline (noise). This constitues a useful model for insurance claims in many circumstances: claims due to natural catastrophes or self-exciting processes exhibit similar features. We give a general account of shotnoise processes with time-inhomogeneous drivers and derive a number ...

Modelling Asset Returns by Lévy Processes

Traditionally, e.g. in Black-Scholes model, are asset returns modelled by processes with conditionally independent, identically normally distributed increments. In this note we present a possibility of using weaker assumptions – modelling the returns by a Lévy process. This allows to capture better the behaviour of stock price dynamics, but on the other hand, parameter estimation and model cali...