Recent work by William Shaw

Key: [JP] Journal Publication;
[SJ] Submitted to Journal for Publication

[B]
Book; [WP] Working Paper;

[CPp]
Conference Presentation (published);
[CPu] Conference presentation (unpublished)

[PJB] Practitioner Journal
or Book article;

****************************

[WP] W.T. Shaw, 2009. Eco-mputational Finance: differential equations for Monte Carlo recycling. Working paper. arXiv:0901.0638v1 [q-fin.CP]

[JP] Yu, E. and Shaw, W.T., 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.

[WP]
Shaw, W.T., 2008, Share price movements in the post-credit-crunch environment (revised Dec 08) PDF. [Key words: Market microstructure, fundamental trader, technical trader, Student distribution, t-distribution, Skew-Student, Pearson Type IV, Fokker-Planck equation, stochastic differential equation, partial differential equation, credit crunch, variance explosion.]

[JP]
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. [Key words: CDS, Credit Default Swaps, Structural Model, Contagion, Credit Crunch.]

[SJ] Dewynne, J.N. and
Shaw, W.T., 2008, Differential Equations and Asymptotic Solutions for
Arithmetic Asian Options: “Black-Scholes formulae” for Asian-Rate Calls, European Journal of Appliued Mathematics Vol 19 (4), 353-391. doi:10.1017/S095679250800750X Journal Link [PDF of preprint]
[Key words: Asian Options, Black-Scholes PDE, Asymptotic expansions, Laplace
transforms, volatility series]

[JP] Steinbrecher, G. and
Shaw, W.T., 2008, Quantile Mechanics, European Journal of Applied Mathematics
Vol 19 (2), pp 87-112, 2008. [Journal Link]. doi:10.1017/S0956792508007341, [Key words: Inverse
CDF, quantile, quantile function, Normal, Student, Beta, T-distribution,
Simulation, Monte Carlo, Inverse Cumulative Distribution Function, non linear
ordinary differential equations, recurrence relations].

[Cpu] Shaw, W.T.,
2007, Dependency without Copulas or Ellipticity, presentation at “Copulae and
Multivariate Probability Distributions in Finance” Warwick, Sept 2007. [PDF]

[Cpu] Shaw, W.T., and Buckley, I.R.C. 2007, The alchemy of probability distributions: beyond
Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank
transmutation map, To appear in the proceedings of the First IMA Conference on
Computational Finance, held March 2007. [PDF]

[JP] W.T. Shaw and K.T.A.
Lee, Bivariate Student t distributions with variable marginal degrees of
freedom and independence, Journal of Multivariate Analysis (2007), doi:10.1016/j.jmva.2007.08.006. [JMVA
link]

[WP] Shaw, W.T., 2007, Refinement of the
Normal Quantile, Simple improvements to the Beasley-Springer-Moro method of
simulating the Normal Distribution, and a comparison with Acklam's method and
Wichura’s AS241, [PDF],
[Mathematica Notebook]
[Key Words, Rational Approximation, Beasley Springer, Moro, Acklam, AS241,
Wichura, Inverse Error function, Normal Quantile, Inverse Cumulative
Distribution Function] (Working paper, updated 20 Feb 07). Also available – (a)
AS241 (Wichura’s method alone) Notebook
and PDF;
(b) Acklam’s method (Notebook
and PDF);
(c) first version of C++ code
for non-linear recursion.

[CPu] Sydney QMF 2006 presentation on
distributional alchemy and related applications of computer algebra to Monte
Carlo methods (Sydney, Australia, Dec 2006) [PDF
of presentation] [Mathematica
Notebook of presentation] [Key Words: Student
Distribution, Distributional alchemy, Cornish Fisher expansion, Gram
Charlier expansion, Skew Normal Distribution]

[JP] Henderson, V.,
Hobson, D., Shaw, W.T., Wojakowski, R., 2006, Bounds for in-progress
floating-strike Asian options using symmetry. Annals of Operations Research
(on-line edition, publ. Nov 18 2006), doi:10.1007/s10479-006-0122-8. Journal Link

[WP] Shaw, W.T., 2006,
A simple resolution of Stokes' paradox. [PDF].
[Key Words: Stokes, Paradox, Fluid Dynamics, Viscous Flow]

[WP] Shaw, W.T., 2006,
Complex Variable Methods for 3D Applied Mathematics: 3D Twistors and the
biharmonic equation. [PDF].
[Key Words: Twistor, Complex Variable, biharmonic, viscous flow]

[WP] Shaw, W.T. and
Lee, K.T.A., 2006, Copula Methods vs Canonical Multivariate Distributions – the
multivariate Student T distribution with general degrees of freedom, November
2006 (submitted) – [April 2007 – some sign errors fixed: PDF].
[Key Words: T Copula, Student Copula, bivariate Student, multivariate Student,
degrees of freedom, elliptical, independence, correlation, dependence, Pearson,
Spearman, Kendall.]

[B] Shaw,
W.T., 2006, Complex Analysis with Mathematica (book), Cambridge University
Press. Publication date April 2006:
CUP
link and further
information.

[JP] Shaw,
W.T., 2006, Sampling Student’s T distribution – use of the inverse cumulative
distribution function. Journal of Computational Finance, Vol 9 Issue 4, pp
37-73, Summer 2006 Journal
Link. On-line
supplements to this article are available here. [Key words: Student, Student’s T
Distribution, T-Distribution, Inverse CDF, Inverse Cumulative Distribution
Function, Quantile, T-Quantile, Simulation, Monte Carlo, Copula]

[JP] Schmitz
Abe, K.E. and Shaw, W.T., 2005, Measure Order of Convergence without an exact
solution, Euler vs Milstein Scheme, International Journal of Pure and Applied
Mathematics, 24 (3), 365-381. [PDF]

[JP] Shaw,
W.T. and Dougan, A.J., 2005, Curvature corrected impedance boundary
conditions in an arbitrary basis, IEEE Transactions on Antennas and
Propagation, 53 (5), 1699-1705, May 2005, doi: 10.1109/TAP.2005.846729 [PDF]

[JP] Shaw, W.T., 2004.
Recovering holomorphic functions from their real or imaginary parts without the
Cauchy-Riemann equations, SIAM Review 46 (4), 717-728, doi: 10.1137/S0036144503432151.
[PDF] A Mathematica
notebook containing demonstrations of how this works, together with additional
functions to manage harmonic conjugates purely algebraically, is also available
as a Mathematica Notebook or in PDF form.

[WP] Shaw, W.T., 2002, Accurate Pricing of
Asian Options by Contour Integration Including Efficient Methods for Low Volatility.
[PDF]
[Mathematica
Notebook]

[CPp] Shaw, W.T., 2001,
Instability of Implied Volatility, Fictitious Skews and Smiles, and the Hazards
of Exotics: The Importance of the Inverse Function Theorem in Mathematical
Finance, in “Disordered and Complex Systems”, ed. P.Sollich, A.C.C. Coolen,
L.P. Hughston, R.F. Streater, (Proceedings of KCL conference, July 2000).

[WP] Shaw, W.T., 2000, A Reply to Pricing
Continuous Asian Options by Fu, Madan and Wang. [PDF] [Mathematica
Notebook]

[PJB] Shaw, W.T., 1999. 'The hazards of I.V. Part III – Convertible
Bonds,' *Financial Products*, Financial
Engineering News, Vol. 2 Issue 9, p. 8.

[PJB] Shaw, W.T., 1999 'The hazards of implied vol. for exotic
options,' *Financial Products*, Financial
Engineering News, Vol. 2 Issue 6, p. 8.

[PJB] Shaw, W.T., 1999 'The league against implied volatility,' *Financial
Products*, Financial Engineering News, Vol. 2 Issue
5, p. 8.

[B] Shaw, W.T., 1998,
Modelling Financial Derivatives with Mathematica, Cambridge University Press

[JP] Shaw, W.T. and Dougan, A.J.,
1998, Green’s function refinement as an approach to radar backscatter: general
theory and applications to low grazing angle scattering from the ocean. IEEE
Transactions on Antennas and Propagation Vol 46 (1), p. 57-66. [PDF]
doi: 10.1109/8.655451

[PJB] Shaw, W.T., 1998, Symbolic Algebra in Derivatives
Modelling, Derivatives Week, Vol 6, (30), p. 6-7.

[PJB] Ghassemieh, R, Shaw, W.T. and Wilson, R., 1997,
Equity-index-linked derivatives, in the Asian Equity Derivatives Handbook,
Euromoney Press.

[JP] Shaw, W.T., Dougan, A.J. and Tough, R.J.A.,
1996 Analytical Expressions for Correlation Functions and Kirchhoff Integrals
for Gaussian Surfaces with Ocean-Like Spectra, *IEEE Transactions on Antennas
and Propagation*, Vol. 44, No. 11,
1454–1463, doi: 10.1109/8.542069 [Journal
Link]

[JP] Shaw, W.T..1995. Symmetric Chaos in the
Complex Plane,' *The Mathematica Journal*, Vol. 5, 3, 84–89. [Journal Link]

[JP] Shaw, W.T. and Dougan, A.J., 1995b Half-space
Green’s functions and applications to scattering of electromagnetic waves from
ocean-like surfaces, *Waves in Random Media*, 5, 341–359 [Journal
Link], doi: 10.1088/0959-7174/5/3/006

[JP] Shaw, W.T. and Dougan, A.J., 1995a, 'The
failure of specular limit formulae for Kirchhoff integrals associated with
Gaussian surfaces with ocean-like spectra,' *Waves in Random Media*, 5, L1–L8. [Journal
Link], doi: 10.1088/0959-7174/5/1/001