Speaker: Dr. Thorsten Rheinlander, London School of Economics

Title: An entropy approach to hedging of derivatives


Date: Thu 20 April, 2006
Time: 14:00
Place: Science Building, Room Z42

Abstract:
(during the actual presentation I will try to make matters much more
accessible)

The goal of this talk is to develop hedging schemes for complex
financial products like derivative securities. This will be done in the
setting of geometric Levy-processes or more general Levy-driven
stochastic volatility models which have shown great flexibility when
fitting a model to observed asset prices. However, the corresponding
financial market then is typically incomplete which results in the
existence of multiple equivalent martingale measures (i.e. pricing
measures). A standard approach is to identify an optimal martingale
measure on the basis of the utility function of the investor. In this
talk we consider the exponential utility function which corresponds via
an asymptotic utility indifference approach to taking the minimal
entropy martingale measure as pricing measure. The density process of
the entropy measure in a general stochastic volatility setting can then
be related to a certain semi-linear integro differential equation. This
presents a unifying framework which covers models like the
Barndorff-Nielsen and Shephard model where both price and volatility
process contain jump terms which are correlated, and also encompasses
the previously studied geometric Levy case or continuous price processes
with an orthogonal volatility process.
It turns out that under quite general conditions the corresponding
utility indifference hedging strategies converge to a mean-variance
optimal hedge under the entropy measure, given that the risk aversion
parameter tends to zero. This establishes a link between utility
indifference hedging and mean-variance hedging under the minimal entropy
martingale measure. Our proposed study is supposed to proceed twofold:
firstly, we will start by specifying the dynamics of the price process
under the statistical measure, and then determine the optimal hedge by
changing to the entropy measure and deriving the optimal mean-variance
hedging strategy; secondly, we will model the price process directly
under a risk-neutral measure, obtained by calibration, and get the
hedging strategy via a Kunita-Watanabe decomposition of the value
process associated with the claim.




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upcoming Science -Math seminars at Koc University.