Monte Carlo Estimation of Greeks
<-- Return to the list
Date: 10-29-2007
Start Time:
6:00pm
End Time: 7:30pm
Speaker: Mike Giles, University of Oxford
Location: 412 Schapiro CEPSR, Davis Auditorium
ABSTRACT
In this talk I will discuss various aspects of computing Greeks through Monte Carlo simulation. I will start by reviewing the three main approaches: finite differences, likelihood ratio method (LRM) and pathwise sensitivity calculation. The last of these leads very naturally to an adjoint implementation which makes it possible to compute the sensitivity to a large number of input parameters at a very low cost, little more than the cost of evaluating the price itself -- this was the topic of my collaboration with Paul Glasserman on "Smoking Adjoints".
The practical development of adjoint codes is greatly
assisted by using Automatic Differentiation (AD) tools. I will explain the underlying ideas and
discuss the use of the FADBAD++ software package which is based on templates
and operator overloading within C++.
The pathwise approach is not applicable when the payoff
is not differentiable. Even when the payoff is differentiable, the use of scripting
in real-world implementations means it can be very difficult in practice to
evaluate the derivative of very complex financial products. To address these
limitations, I will present a new idea to combine the adjoint pathwise approach
for the stochastic path evolution with LRM for the payoff evaluation.
BIO
Mike Giles is a professor of scientific computing at the University of Oxford. After many years of developing new algorithms in computational fluid dynamics with applications to aircraft engine design, he has recently moved into computational finance working on both Monte Carlo and finite difference methods. He and Paul Glasserman were name Quants of the Year 2007 by Risk magazine for their research on the use of adjoint techniques for efficient Monte Carlo estimation of Greeks.