Reading List

Reading List

History

Boyle, Phelim P. (1977) "Options: A Monte Carlo approach", Journal of Financial Economics 4, 323-338.

Metropolis, N. (1987) "The beginning of the Monte Carlo method", Los Alamos Science.

Rao, C. R. (1989) Statistics and Truth. New Delhi: Council of Scientific & Industrial Research.

Siniksaran, Enis (2008) "Throwing Buffon's needle with Mathematica", Mathematica Journal 11(1), 71-90.

Random number generation

Brent, Richard P. (2004) "Fast and reliable random number generators for scientific computing", .

Brent, Richard P. (2004) "Note on Marsaglia's Xorshift random number generator", Journal of Statistical Software 11(5), 1-5.

Entracher, Karl (1997) "A collection of selected pseudorandom number generators with linear structures", .

Gentle, James E. (2003) Random number generation and Monte Carlo methods. New York, NY: Springer.

Knuth, Donald E. (1998) The art of computer programming, Volume 2: Seminumerical algorithms. Reading, MA: Addison Wesley Longman.

Marsaglia, George (2003) "Xorshift RNGs", Journal of Statistical Software 8, 1-9.

Matsumoto, Makoto, and Takuji Nishimura (1998) "Mersenne Twister: A 623-dimensionallly equidistributed uniform pseudorandom number generator", ACM Transactions on Modeling and Computer Simulations.

McCullough, B. D. (2008) "Microsoft Excel's 'Not the Wichmann-Hill' random number generators", Computational Statistics and Data Analysis 52, 4587-4593.

Microsoft Corporation "Description of the RAND function in Excel 2007 and in Excel 2003".

Press, William H., Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery (2007) Numerical recipes: The art of scientific computing. Cambridge: Cambridge University Press.

Soto, Juan (1999) "Statistical testing of random number generators", "Proceedings of the 22nd. National Information Systems Security Conference", .

Tajima, Akira , Syoiti Ninomiya , Shu Tezuka On the anomaly of RAN1() in Monte Carlo pricing of financial derivatives , J.M. Charnes , D.J. Morrice , D.T. Brunner , and J.J Swain Proceedings of the 1996 Winter Simulation Conference (1996)

Walker, John "Hotbits: Genuine random numbers, generated by radioactive decay".

Non-uniform distributions

Acklam, P. J. "An algorithm for computing the inverse normal cumulative distribution function ".

Beasley, J. D., and S. G. Springer (1977) "Algorithm AS 111: The percentage points of the normal distribution", Applied Statistics 26(1), 118-121.

Brophy, Alfred L. (1985) "Approximation of the inverse normal distribution function", Behaviour Research Methods, Instruments, & Computers 17(3), 415-517.

Devroye, Luc (1986) Non-uniform random variate generation. Springer-Verlag.

Doornik, Jurgen A. (2005) "An improved Ziggurat method to generate normal random variables", .

Gentle, James E. (2003) Random number generation and Monte Carlo methods. New York, NY: Springer.

Hörmann, Wolfgang, and Josef Leydold (2003) "Continuous random variate generation by fast numerical inversion", ACM Transactions on Modeling and Computer Simulation 13, 347-362.

Leva, J. L. (1992) "A fast normal random number generators", ACM Transactions on Mathematical Software 18(4), 449-453.

Marsaglia, George, and T. A. Bray (1964) "A convenient method for generating normal variables", SIAM review 6(3), 260-264.

Marsaglia, George, Arif Zaman, and John C. W. Marsaglia (1994) "Rapid evaluation of the inverse normal distribution function", Statistics and Probability Letters 19, 259-266.

Marsaglia, George., and W. W. Tsang (2000) "The ziggurat method for generating random variables", Journal of Statistical Software 5, 1-7.

Moro, Boris (1995) "The full monte", Risk 8, 57-58.

Press, William H., Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery (2007) Numerical recipes: The art of scientific computing. Cambridge: Cambridge University Press.

Shaw, William "Refinement of the normal quantile".

Thomas, David B., Wayne Luk, Philip H. W. Leong, and John D. Villasenor (2007) "Gaussian random number generators", ACM Computing Surveys 39(4).

Wichura, Michael J. (1988) "Algorithm AS 241: The percentage points of the normal distribution", Applied Statistics 37(3), 477-484.

Variance reduction

Boyle, Phelim P., Mark Broadie, and Paul Glasserman (1997) "Monte Carlo methods for security pricing", Journal of Economic Dynamics and Control 21, 1267-1321.

Glasserman, Paul (2003) Monte Carlo methods in financial engineering. New York, NY: Springer.

Jäckel, Peter (2002) Monte Carlo methods in finance. Chichester: Wiley.

McLeish, Don L. (2005) Monte Carlo methods and finance. Hoboken, N.J.: Wiley.

Low discrepancy sequences

Anderson, Philip, and Fred Guterl (1994) "Suddenly, number theory makes sense to industry", Businessweek, 20 June.

Bratley, Paul, and Bennett L. Fox (1988) "Algorithm 659: Implementing Sobol's Quasirandom sequence generator", ACM Transactions on Mathematical Software 14(1), 88-100.

Carter, Michael (2011) "A toolbox for quasi-random simulation", The Mathematica Journal 13(30 December).

Galanti, Silvio, and Alan Jung (1997) "Low-discrepancy sequences: Monte Carlo simulation of option prices", Journal of Derivatives 5(5), 63-83.

Glasserman, Paul (2003) Monte Carlo methods in financial engineering. New York, NY: Springer.

Hickernell, Fred J., Christiane Lemieux, and Art B. Owen (2005) "Control variates for quasi-Monte Carlo", Statistical Science 20(1), 1-31.

Joe, Stephen, and Frances Y. Kuo (2003) "Remarks on algorithm 659: Implementing Sobol's quasirandom sequence generator", ACM Transactions on Mathematical Software 29(1), 49-57.

Joe, Stephen, and Frances Y. Kuo (2008) "Constructing Sobol sequences with better two-dimensional projections", SIAM Journal of Scientific Computing 30, 2635-2654.

Jäckel, Peter (2002) Monte Carlo methods in finance. Chichester: Wiley.

L'Ecuyer, Pierre (2009) "Quasi-Monte Carlo methods with applications in finance", FFinance and Stochastics 13, 307-349.

Lemieux, Christiane (2009) Monte Carlo and quasi-Monte Carlo sampling. New York, NY: Springer.

Morokoff, William J., and Russel E. Caflisch (1994) "Quasi-random sequences and their discrepancies", SIAM Journal on Scientific Computing 15, 1251-1279.

Papageorgiou, A (2002) "The Brownian bridge does not offer a consistent advantage in quasi-Monte-Carlo integration", Journal of Complexity.

Papageorgiou, A., and J. Traub (1996) "Beating Monto Carlo", Risk 9, 63-65 (Online as 'New results in deterministic pricing of financial derivatives').

Press, William H., Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery (2007) Numerical recipes: The art of scientific computing. Cambridge: Cambridge University Press.

Sobol, I.M. (1998) "On quasi-Monte Carlo integrations", Mathematics and Computers in Simulation 47, 103-112.

Wang, Xiaoqun, and Ian H. Sloan (2005) "Why are high-dimensional finance problems often of low effective dimension", SIAM Journal of Scientific Computing 27(1), 159-183.

Sensitivity analysis

Broadie, Mark and Paul Glasserman (1996) "Estimating security price derivatives using simulation." Management Science 42, 269-285.

Glasserman, Paul (2003) Monte Carlo methods in financial engineering. New York, NY: Springer.

American-style derivatives

Andersen, Leif, and Mark Broadie (2004) "Primal-dual simulation algorithm for pricing multdimensional American options", Management Science 50(9), 1222-1234.

Broadie, Mark, and Menghui Cao (2008) "Improved lower and upper bound algorithms for pricing American options by simulation", .

Caflisch, Russel E. , Suneal Chaudhary Monte Carlo methods for American options , R. G. Ingalls , M.D. Rossetti , J.S. Smith , and B.A. Peters Proceedings of the 2004 Winter simulation conference

Chaudary, Suneal K. (2005) "American options and the LSM algorithm: quasi-random sequences and Brownian bridges", Journal of Computational Finance 8(4).

Fu, Michael C, Scott B. Laprise, Dilip B. Madan, Yi Su, and Rongwen Wu (2000) "Pricing American options: A comparison of Monte Carlo simulation approaches", .

Garcia, Diego (2003) "Convergence and bias of Monte Carlo estimates of American option prices using a parametric rule", Journal of Economic Dynamics and Control 27, 1855-1879.

Glasserman, Paul (2003) Monte Carlo methods in financial engineering. New York, NY: Springer.

Longstaff, Francis A., and Eduardo S. Schwartz (2001) "Valuing American options by simulation: A simple least-squares approach", Review of Financial Studies 14(1), 113-147.

Non-Gaussian processes

Cont, Rama, and Peter Tankov (2004) Financial modelling with jump processes. Boca Raton, FL: Chapman & Hall/CRC.

Glasserman, Paul (2003) Monte Carlo methods in financial engineering. New York, NY: Springer.

Joshi, Mark S (2003) The concepts and practice of mathematical finance. Cambridge, U.K, New York: Cambridge University Press.

Kou, S. G. Jump-diffusion models for asset pricing in financial engineering , J.R. Birge , and V. Linetsky Handbooks in OR & MS Elsevier (2008) 15 73-116

Tankov, Peter, and Ekaterina Voltchkova "Jump-diffusion models: a practitioner's guide", .

Exotic options

Asian options

Boyle, Phelim, and Alexander Potapchik (2008) "Prices and sensitivities of Asian options: A survey", Insurance: Mathematics and Economics 42, 189-211.

Curran, Michael (1994) "Valuing Asian and portfolio options by conditioning on geometric mean price", Management Science 40(12), 1705-1711.

Joshi, Mark S. (2009) Graphical Asian options.

Ju, Nengjiu (2002) "Pricing Asian and basket options via Taylor expansions", Journal of Computational Finance 5(3), 79-103.

Nielsen, J. Aase, and Klaus Sandmann (2003) "Pricing bounds on Asian options", Journal of Financial and Quantitative Analysis 38(2), 449-473.

Vanmaele, M., G. Deelstra, J. Liinev, J. Dhaene, and M. J. Goovaerts (2006) "Bounds for the price of discrete arithmetic Asian options." Journal of Computational and Applied Mathematics 185: 51-90.

Spread options

Alexander, Carol, and Venkatramana (2007) "Analytic approximations for spread options", .

Carmona, René, and Valdo Durrleman (2003) "Pricing and hedging spread options", SIAM Review 45(4), 627-685.

Bjerksund, Petter, and Gunnar Stensland (2006) Closed form spread option valuation.

Risk management

Value at risk

Glasserman, Paul (2003) Monte Carlo methods in financial engineering. New York, NY: Springer.

Holton, Glyn A. (2013). Value-at-Risk: Theory and Practice, 2nd ed. e-book at http://value-at-risk.net.

Excel

Brenner, Richard "Names".

Dalton, Steve (2007) Financial applications using Excel add-in development in C/C++. Chichester, U.K.: Wiley.

Frontline Systems "Controlling Solver with VBA".

Jackson, Mary, and Mike Staunton (2001) Advanced modelling in finance using Excel and VBA. Chichester: Wiley.

Microsoft "XL: Method Used by Goal Seek to Find a Solution, KB100782."

Roman, Steven (2002) Writing Excel macros with VBA. Sebastopol, CA: O'Reilly.