MF2:
Computational Finance:
2011-2012
Programme
Prof William Shaw
Back to William Shaw's home
page
The London
Graduate School in Mathematical Finance
This is the
fourth year we are running a programme of lectures within this joint initiative
now involving Brunel, King's, Imperial, Birkbeck, the LSE and University College. The programme provides world
class instruction to doctoral students in mathematical finance working in
London University.
MF2:
Computational Finance: Where and When
Provisionally, Tuesdays, 2pm to
4pm in October, November and December 2011. Location: UCL (start date and room TBC).
MF2:
Computational Finance: About the Course
Computer
Languages employed: C++ and Mathematica (twin track presentation); some special topics with GridMathematica and CUDA.
Background
In modern
mathematical finance, the use of computers goes far beyond their traditional
use for purely numerical work, and it is now wholly out of date to think of
computers entirely for number crunching, or indeed to just use computer
languages that are only capable of numerical calculations. Mathematical finance
involves the calculations of expectations by some form of integration, the
calculation of many quantities of interest requires differentiation, and
practical calculations often involve the solution of partial differential
equations. Many calculations involve large amounts of manipulation. Modern work
is therefore best done in environments where it is possible to do symbolic
manipulations alongside efficient numerical work. This must of course be
balanced against the needs of industry, where one frequently finds more
traditional tools in use. Then, especially for risk management purposes, it is
appropriate to make detailed comparisons between analytical solutions and their
numerical analogues.
The emphasis
therefore will be on useful modern computational methods, including numeric,
symbolic and parallel (grid or GPU) methods.
Numerical methods will be approached from the point of view of their accuracy
and mathematical integrity, and links to numerical analysis. This course will
not be looking at code-structuring or IT integration issues (which tend to be
very institution-specific) nor will be looking at anything related to
particular operating systems or hardware platforms. It will be given in based on C++, Mathematica and CUDA.
The course will
recognize that the use of computers for modelling in the financial industry can
take various forms. Intensive numerical methods in pricing and hedging tools in
daily use in institution-wide systems will often be implemented in C++. Advanced mathematical techniques
may require a combination of exotic special functions, complex variable methods
and computer algebra and calculus. Risk management and rapid prototyping teams
may require flexible on-desk tools for implementing models quickly on a one-off
basis.
Platform: The ideal situation is for students to bring their own laptop pre-configured with eduroam internet access, in order to download material brought up in lectures.
First lectures:
1. Introduction + Simulation via quantiles
2. Quick introduction to C++
Ideally you will have available a C++ compiler on your laptop or computer elsewhere. If you have programmed before, e.g. in MS Visual studio, you are welcome to use that, but if you are new to this type of coding I encourage you to try the Dev-cpp tool (see below) which is very friendly to beginners.
C++ Programming Material
I am using the C++ development environment Dev-cpp from www.bloodshed.net, running under Windows.
Mark Joshi's web page that goes with his book Design Patterns and Derivatives Pricing is here. It has a link where you can download his code as a zip file. You might also like to take a look at his tools for linking C++ models to Excel. He supports the Dev-cpp environment with pre-made project files. See the section on Software downloads on this page.