Development of Multilevel Monte Carlo Algorithms for Mathematical Finance

Lead Research Organisation: University of Oxford
Department Name: Computer Science

Abstract

This Springboard Fellowship will help me enormously in my mid-career move into computational finance after 20 years of computational fluid dynamics, simulating the flow through aircraft gas turbine engines. The research topic concerns the pricing of financial derivatives options (based on equities, commodities, interest rates and exchange rates) using Monte Carlo methods which evaluate the average outcome from multiple simulations of possible future evolution subject to random inputs. This research area, the solution of stochastic differential equations, is a major growth area in mathematics, and it underpins much of the everyday working of the major banks in London, which in turn form a large part of the UK economy.Six months ago, I had an idea which signifiantly reduces the computational cost of the Monte Carlo calculations required to achieve a given accuracy. My preliminary research results, and numerical tests on model problems, are very encouraging. It has been well received by leading academic figures and has already led to invitations for three university presentations and four seminars at investment banks. My objective with this Fellowship proposal is to build on this initial success by further developing the numerical technique, which I refer to as the multilevel Monte Carlo method, to enhance its performance and make it competitive against the leading methods used today in the industry. Alongside the research itself, a major goal of the fellowship is to build collaborations with key academics worldwide and with leading banks in London. My aim is that these should continue long after the end of the Fellowship, with the banks being my major source of funding for subsequent research. Also, as I am still very new to this field of research, there are deficiencies in my understanding of the stochastic analysis theory which underpins this field and I will work to address these.
 
Description The multilevel Monte Carlo method provides a huge improvement in the efficiency of Monte Carlo simulation in a wide variety of contexts. It has led to a new substantial research effort worldwide, as documented in the URL below.
Exploitation Route A follow-on project is developing and applying the methodology to the simulation of nuclear waste repositories.
Sectors Financial Services/ and Management Consultancy

URL http://people.maths.ox.ac.uk/gilesm/mlmc_community.html
 
Description Multilevel Monte Carlo Methods for Elliptic Problems with Applications to Radioactive Waste Disposal
Amount £550,000 (GBP)
Funding ID EP/H05183X/1,EP/H051503/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Academic/University
Country United Kingdom
Start 07/2010 
End 06/2013