3:30 p.m., Friday
Dilip B. Madan
Robert H. Smith School of Business
University of Maryland
Levy Processes in Financial Modeling
We investigate the relative importance of diffusion and
jumps in a new jump diffusion model for asset returns.
In contrast to the standard modelling of jumps for asset
returns, the jump component of our process can display
finite or infinite activity, and finite or infinite variation.
Empirical investigations of time series indicate that index
dynamics are essentially devoid of a diffusion component,
while this component may be present in the dynamics of
individual stocks. This result leads to the conjecture
that the risk-neutral process should be free of a diffusion
component for both indices and individual stocks. Empirical
investigation of options data tends to confirm this conjecture.
We conclude that the statistical and risk-neutral processes
for indices and stocks tend to be pure jump processes of
infinite activity and finite variation.