MF2: Computational Finance:

2010-2011 Programme

Prof William Shaw

King’s College, London

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The London Graduate School in Mathematical Finance

This is the third year we are running a programme of lectures within this joint initiative involving King’s, Imperial, Birbeck and the LSE. The programme provides world class instruction to doctoral students in mathematical finance working in London University. For further details see the LGS home page.

MF2: Computational Finance: Where and When

Tuesdays, 3pm to 5pm in October, November and December 2010. Location Room K4.33 (also known as 22DB), The Strand Building, King’s College. MF2 starts on Tuesday October 12th 2010.

DIRECTIONS!

Enter the Strand building (map) from the Strand and take the lift to the 5^th (FIFTH Floor). There are signs to PAWS room K4.33 (formerly 22DB) from the exit to the lifts on the 5^th floor. Students from Birkbeck, Imperial, LSE will need me to let them in.

MF2: Computational Finance: About the Course

Computer Languages employed: C++ and Mathematica (twin track presentation); some special topics with GridMathematica, CUDA/OpenCL.

Course Introduction and Topics

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finance, the use of computers goes far beyond their traditional use for purely numerical work, and it is now wholly out of date to think of computers entirely for number crunching, or indeed to just use computer languages that are only capable of numerical calculations.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) 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 a computer classroom equipped with computers supporting C++, Mathematica and other software and make use of whatever tools are most convenient.

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.