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.
Organisations
People |
ORCID iD |
Mike Giles (Principal Investigator) |
Publications
Giles M
(2008)
Multilevel Monte Carlo Path Simulation
in Operations Research
Giles M
(2008)
Monte Carlo and Quasi-Monte Carlo Methods 2006
Giles M
(2009)
Multilevel Monte Carlo for basket options
Giles M
(2009)
Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff
in Finance and Stochastics
Giles M
(2012)
Stochastic Finite Differences and Multilevel Monte Carlo for a Class of SPDEs in Finance
in SIAM Journal on Financial Mathematics
Giles M
(2013)
Monte Carlo and Quasi-Monte Carlo Methods 2012
Giles M
(2013)
Monte Carlo and Quasi-Monte Carlo Methods 2012
Giles M
(2014)
Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulation
in The Annals of Applied Probability
Lester C
(2015)
An adaptive multi-level simulation algorithm for stochastic biological systems.
in The Journal of chemical physics
Vidal-Codina F
(2015)
A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations
in Journal of Computational Physics
Giles M
(2015)
Multilevel Monte Carlo Approximation of Distribution Functions and Densities
in SIAM/ASA Journal on Uncertainty Quantification
Giles M
(2015)
Multilevel Monte Carlo methods
in Acta Numerica
Vidal-Codina F
(2016)
An Empirical Interpolation and Model-Variance Reduction Method for Computing Statistical Outputs of Parametrized Stochastic Partial Differential Equations
in SIAM/ASA Journal on Uncertainty Quantification
Lester C
(2016)
Extending the Multi-level Method for the Simulation of Stochastic Biological Systems.
in Bulletin of mathematical biology
Giles M
(2017)
Multilevel Monte Carlo for exponential Lévy models
in Finance and Stochastics
Giles M
(2018)
Random Bit Quadrature and Approximation of Distributions on Hilbert Spaces
in Foundations of Computational Mathematics
Katsiolides G
(2018)
Multilevel Monte Carlo and improved timestepping methods in atmospheric dispersion modelling
in Journal of Computational Physics
Giles M
(2019)
Multilevel Nested Simulation for Efficient Risk Estimation
in SIAM/ASA Journal on Uncertainty Quantification
Hironaka T
(2020)
Multilevel Monte Carlo Estimation of the Expected Value of Sample Information
in SIAM/ASA Journal on Uncertainty Quantification
Fang W
(2020)
Adaptive Euler-Maruyama method for SDEs with nonglobally Lipschitz drift
in The Annals of Applied Probability
Croci M
(2021)
Multilevel Quasi Monte Carlo Methods for Elliptic PDEs with Random Field Coefficients via Fast White Noise Sampling
in SIAM Journal on Scientific Computing
Fang W
(2022)
Multilevel and Quasi Monte Carlo Methods for the Calculation of the Expected Value of Partial Perfect Information.
in Medical decision making : an international journal of the Society for Medical Decision Making
Giles M
(2023)
MLMC techniques for discontinuous functions
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 | Public |
Country | United Kingdom |
Start | 06/2010 |
End | 06/2013 |