An Historical Perspective

• Fooled by Randomness, N. Taleb, (2001) Texere, New York, ISBN 1-58799-071-7

• Derivatives: The tools that changed finance, P. Boyle, F. Boyle, (2001) Risk Books, ISBN 1-899-332-88

• Rogue Trader: How I brought down Barings Bank and shook the financial world, N. Leeson, (1996) Little Brown and Company

• "How the Eggheads Cracked," New York Times Magazine, January 24, 1999.

• When genius failed: the rise and fall of Long Term Capital Management, R. Lownenstein (2000), Random House

• Inventing Money: The story of Long Term Capital and the legends behind it, N. Dunbar, Wiley, Chichester (2000).

• Big bets gone bad: Derivatives and bankruptcy in Orange County, P. Jorian, Academic Press, New York (1995).

• How Long Term Lost its Capital, P. Jorian, Risk, September, 1999.

• Using VAR to control risk: how wrong can you be?, X. Ju and N. Pearson, J. of Risk, 1, no. 2 (Winter 1998/9), 5-36.

Real options

• Real Options: managerial flexibility and strategy in resource allocation, L. Trigeorgis (1996), MIT Press, ISBN 0-262-20102-X

• Investment under uncertainty, Dixit and Pindyck, (1994), Princeton University Press, Princeton, ISBN 0-691-03410-9

General Books which have some numerical algorithms

• Paul Wilmott on Quantitative Finance, P. Wilmott (2000), Wiley, ISBN 0-471-87438-8 (2 vols)

• Option Pricing, P. Wilmott, J. Dewynne, S. Howison (1993), Oxford Financial Press, ISBN 0-9522082-0-2

Books which cover Monte Carlo and PDE Methods

• Tools for Computational Finance, R. Seydel (2002), Springer-Verlag, ISBN 3-540-43609-X

• An Introduction to Financial Option Valuation, D. Higham, Cambridge University Press, 2004

• Pricing Financial Instruments: the Finite Difference Method, D. Tavella and C. Randall (2000), Wiley, ISBN 0-471-19760-2.

• Monte Carlo Methods in Financial Engineering, P. Glasserman, Springer, New York, 2003.

War stories from the trading desk

• Dynamic Hedging, N. Taleb, (1997), Wiley, ISBN 0-471-15280-3.

Monte Carlo

• Brately and Fox, Algorithm 669: Implementing Sobol's quasi random sequence generator, ACM Trans. Math. Soft. 14:88-100, 1988.

• Brately, Fox, Niederreiter, Implementation and test of low-descrepancy sequences, ACM Trans. Modelling Simulation 2(3):195-213,1992.

• Brodie and Glasserman, Monte Carlo methods for security pricing, J. Econ. Dyn. Con. 21:1267-1321, 1997.

• Brodie and Glasserman, Estimating security price derivatives using simulation, Man. Sci. 42:269-285, 1996.

• Fox, Algorithm 647: Implementation and relative efficiency of quasi-random sequence generators, ACM Trans. Math, Soft. 12(4):362-376, 1986.

• Glasserman, Zhao, Fast Greeks by simulation in forward Libor models, J. Comp. Fin., 3:5-40 (Fall, 1999).

• Glasserman, Monte Carlo Methods in Financial Engineering, Springer, New York, 2003.

• Halton, On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals, Nuericshe Mathematik, 2:84-90, 1960.

• F. Longstaff and E. Schwartz, Valuing American Options by simulations: a simple least squares approach, Review of Financial Studies, vol 14, no 1 (2001) 113-147.

• M. Moreno and Javier F. Navas, On the robustness of the least-squares Monte Carlo (LSM) for pricing American Derivatives (available from Javier Navas website, http://profesores.ie.edu/jfnavas)

• Neiderreiter, Random number generation and quasi-monte carlo methods, SIAM, 1992.

• Press et al, Numerical Recipes in C , Cambridge University Press, 1992.

• Sobol, The distribution of points in a cube and the approximate evaluation of integrals, USSR Comp. Math, and Math, Phys., 7(4):86-112, 1967.

• Tezuka, Polynomial arithmetic analogue of Halton sequences, ACM Trans. Modelling Simulation, 3:99-107,1993

Numerical PDE

• For applications to finance, see my web page. You can download several pdf tech reports.

• Course notes in the DC library for CS774 has an extensive list of PDE references.

• Pricing Financial Instruments: the Finite Difference Method, D. Tavella and C. Randall (2000), Wiley, ISBN 0-471-19760-2.

• Computational differential equations, E. Eriksson, D. Estep, P. Hansbo, C. Johnson, (1996), Cambridge, QA371.5D37C66, ISBN 0-521-56738-6.

• Numerical schemes for conservation laws D. Kroner (1997) QA 377.K74.

• Numerical solution of Partial Differential equations}, K. Morton and D, Mayers, Cambridge University Press, QA377.M69 (1994), ISBN 0-521-42922-6.

• Numerical Analysis of Partial Differential Equations, Hall and Porsching, Prentice Hall, Toronto QA374.H29 (1990).

• Numerical methods for conservation laws}, R.J. LeVeque, (1990) QA377.L4157.

• Numerical Solution of Partial Differential Equations, G.D. Smith - Oxford University Press, QA374.S56 (1985).

• Numerical Methods for Partial Differential Equations, W.F. Ames. QA374.A46 (1992).

• Numerical Solution of Partial Differential Equations in Science and Engineering, Lapidus and Pinder, Q172.L36 (1982)

• Finite Element Solution of Boundary Value Problems, Axelsson and Barker (1984), QA379.A9.