Recent work by William Shaw
[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[CPp] Conference Presentation (published); [CPu] Conference presentation (unpublished)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.]
[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.
[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).
[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