Department of Systems Engineering and Engineering Management,

                    The Chinese University of Hong Kong


Local Volatility Function Models under a Benchmark Approach

Eckhard Platen
University of Technology Sydney

Date : June 9, 2006 (Friday)

Time : 4:30 p.m. - 5:30 p.m.

Venue : Room 513, William M.W. Mong Engineering Building

(Engineering Building Complex Phase 2), CUHK

Without requiring the existence of an equivalent risk neutral probability
measure this paper studies a class of one-factor local volatility function
models for stock indices under a benchmark approach. It is assumed that the
dynamics for a large diversified index approximates that of the growth optimal
portfolio. Fair prices for derivatives when expressed in units of the index
are martingales under the real world probability measure. Different to the
classical approach that derives risk neutral probabilities the paper obtains
the transition density for the index with respect to the real world
probability measure. Furthermore, the Dupire formula for the underlying local
volatility function is recovered without assuming the existence of an
equivalent risk neutral probability measure. A modification of the constant
elasticity of variance model and a version of the minimal market model are
discussed as specific examples together with a smoothed local volatility
function model that fits a snapshot of S&P500 index options data.

Eckhard Platen is a Professor of Quantitative Finance at the University of
Technology, Sydney. Prior to this appointment he was Head of the Centre for
Financial Mathematics in the Institute of Advanced Studies at the Australian
National University and is Adjunct Professor of this University. He has a PhD
in Mathematics from the Technical University in Dresden and obtained his Dr Sc
from the Academy of Sciences in Berlin. He is co-author of two well-known
books on numerical methods for stochastic differential equations at Springer
Verlag and has authored more than hundred papers in finance and applied
mathematics. He serves on the editorial boards of five international journals
in finance and applicable mathematics. His current research interests cover
areas ranging from financial market modeling, portfolio optimization,
derivative pricing and dynamic risk analysis to numerical methods in finance.
He initiated and has been co-organizing the annual Quantitative Methods in
Finance conference series.


Note : Cookies and drinks will be available at 4:15 pm.



                       ***** ALL ARE WELCOME *****

Host : Prof. Xunyu Zhou
Tel : 2609 8238
Email : xyzhou@se.cuhk.edu.hk

For more information please

refer to http://www.se.cuhk.edu.hk/~seg5810/