King's College London Financial Mathematics |

Department of Mathematics
Room 532, Strand Building |

**London Graduate School 2010-11**: course information for MF2 computational finance available here.

**KCL MSc FM06 Numerical and Computational Methods in Finance**: course information available here. See your e-mail for log-in information. Note that FM06 is a "pen-and-paper" course providing the theory of numerical financial computation. FM12 in S2 is the practical course.

**Portfolio Optimization for general risk measures**
Suppose you want to optimize a (long) portfolio with regard to any one of a number of risk measures (Mean-Variance, VaR, CVaR, Utility etc.). Here is a solution using *random portfolios*. SSRN.

**Presentation at NERC-KTN Risk Visualization Workshop.**
My presentation on risk visualization given at the workshop held at Lloyds on May 11th can be downloaded as both a live Mathematica notebook and PDF. It shows how to work out VaR and CVaR (expected tail loss) for Student and Normal Distributions, for various power law behaviour and event frequency, and also corrects Felix Salmons's Wired Magazine story on Gaussian copulas.

William Shaw joined the Financial Mathematics Group as Professor in 2006. He received his doctorate in mathematics from the University of Oxford, following which he held post-doctoral positions at the University of Cambridge and M.I.T. He then worked as a consultant applied and financial mathematician before joining the Quantitative Analysis Group of Nomura International plc, where he was a specialist in computational finance and equity derivatives modelling. At the same time he held a post as College Lecturer at Balliol College, Oxford. He was later Fellow and Tutor in Applied Mathematics at St. Catherine's College, Oxford, while also University Lecturer in Mathematical Finance and Academic Director of the Oxford Diploma and MSc in Mathematical Finance.

Professor Shaw directs the KCL Centre for Financial Grid Computing, which is a member of the Apple Research and Technology Support (ARTS) programme. His research interests include: Fat-tailed distributions and their financial origins; The theory of quantiles for Monte Carlo simulation; Applications of complex analysis to finance and applied mathematics; Performance indicators for stock selection, including robust and genetic approaches; Optimization; Convertible bonds; Computational finance, especially symbolic methods. From time to time he also works on fluid mechanics, applied electromagnetics, complex variables and twistor models of string theory. He has written 3 books on applications of computer algebra, including "Modelling Financial Derivatives with Mathematica". He is a Fellow of the Institute of Mathematics and its Applications and is co-editor in chief of Applied Mathematical Finance. He is also an Associate Editor of the International Journal of Theoretical and Applied Finance and a member of the Scientific Committee for the Knowledge Transfer Network in Industrial Mathematics.

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CUDA and Computational Finance at King's
**: You can get my presentation from the Dec 2009 CUDA workshop and example GPU quantile codes here. Suggestions for going faster welcome. The KCL **Centre for Financial Grid Computing** is grateful to Nvidia Corporation for their generous donation of Quadro GPUs for research into advanced GPU-based parallel computation, and to Professor Claudio Albanese for his work on this and related projects. Further information is available here

**KCL MSc students win Marshall Wace Quant Challenge!** A team of financial maths MSc students has won the first "Quant Challenge" run by the hedge fund Marshall Wace. Read more about the Challenge.

**Maths and the Financial Crisis** The Financial Times of 10th June 2009 contains a story on our letter to Lord Turner, Chairman of the FSA. For my own commentary on the situation, and a summary of the long history of mathematicians trying to persuade banks to use (non-Gaussian) fat-tailed models for risk assessment, see here.

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Applied Mathematical Finance
** Prof. Shaw is Co-Editor in Chief of the journal Applied Mathematical
Finance. E-mail papers for submission to here.

** Recent working paper(s) (recent arXiv uploads)
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Shaw, W.T. 2010, Complex Variable Methods for 3D Applied Mathematics: 3D Twistors and the biharmonic equation: preprint.

Shaw, W.T., 2009, A model of returns for the post-credit-crunch reality: Hybrid Brownian motion with price feedback. Submitted (revised Aug 09). ArXiv link.

W.T. Shaw and J. McCabe, 2009. Monte Carlo sampling given a Characteristic Function: Quantile Mechanics in Momentum Space. arXiv:0903.1592v1 [q-fin.ST]

W.T. Shaw and N. Brickman, 2009. Differential equations for Monte Carlo recycling and a GPU-optimized Normal quantile. Working paper. arXiv:0901.0638v3 [q-fin.CP]

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Recent journal papers:
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W.T. Shaw and A. Munir, 2009. *Dependency without Copulas or Ellipticity*, European Journal of Finance, doi: 10.1080/13518470802697402 Journal link.

E. Yu & W.T. Shaw, 2009, *On the valuation of derivatives with snapshot reset features*. International Journal of Theoretical and Applied Finance, Vol 11, Issue 8, 905-941. doi 10.1142/S0219024908005081, Journal Link.

Haworth, H., Reisinger, C., and Shaw, W.T., 2008, *Modelling Bonds & Credit Default Swaps using a Structural Model with Contagion*. Quantitative Finance, Vol 8 No 7, 669-680. doi:10.1080/14697680701834614, Journal Link.

J.N. Dewynne and W.T. Shaw, 2008, *Differential equations and asymptotic solutions
for arithmetic Asian options: `Black-Scholes
formulae' for Asian rate calls*, European Journal of Applied Mathematics Vol 19 (4), pp 353-391. doi:10.1017/S095679250800750X Journal Link.

G. Steinbrecher and W.T. Shaw, 2008, *Quantile Mechanics*, European Journal of Applied Mathematics Vol 19 (2), pp 87-112. doi:10.1017/S0956792508007341 Journal Link.

All recent publications in chronological order.

Also see my page on Quantile Functions.

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Books by WT Shaw
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Complex Analysis with Mathematica. Every year The American Library Association gives a number of books the award of "Outstanding Academic Title" status in their review publication Choice. "Complex Analysis with Mathematica" has been given this accolade in the January 2008 edition of Choice. The book was also reviewed in their September 2007 edition, where it was described as a "truly next-generation book" and "Essential". Further information about the book is available here.

Modelling Financial Derivatives with Mathematica.

Mathematical Finance - Mathematica Notebooks

Twistors and Strings. (Enabled Jan 2007).

*Research Students and Projects.

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Maths in the Media:
Media and Chemistry make bad maths smell...
**

The BBC ran a story based on the Royal Society of Chemistry saying British maths is bad 'coz the Chinese do harder geometry. Oh dear. Read the real story here.

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Mathematical Finance News:
Has Gordon Brown finally owned up?
**

The April 25th edition of "Metro" carries the following story, following the Chancellor's visit to Chorlton High School in Manchester. Metro claims that Gordon told a school pupil: "I did maths at school and for one year at university but I don't think I was ever very good at it - and some people would say it shows." The BBC also reported this story here.