Monte Carlo and Quasi-Monte Carlo Simulation

Is this chapter we will learn the basics of pricing derivatives using simulation methods. We will consider both Monte-Carlo and quasi-Monte Carlo but – of course – with a special emphasis on the latter. The aim of our exposition is not to provide a large toolbox for the quantitative analyst, but to help getting started with the topic. QMC-pricing is an active area of research by its own and the reader is encouraged to consult the specialized literature. We will, however, take a look at some popular examples that frequently serve as benchmarks for refined simulation techniques.

[1]  J. Dick,et al.  Discrepancy bounds for deterministic acceptance-rejection samplers , 2014 .

[2]  Stefan Heinrich,et al.  Multilevel Monte Carlo Methods , 2001, LSSC.

[3]  Eichler Andreas,et al.  Calibration of financial models using quasi-Monte Carlo , 2011 .

[4]  Michael B. Giles,et al.  Multilevel Monte Carlo Path Simulation , 2008, Oper. Res..

[5]  Paul Glasserman,et al.  Monte Carlo Methods in Financial Engineering , 2003 .

[6]  Ian H. Sloan,et al.  Quasi-Monte Carlo Methods in Financial Engineering: An Equivalence Principle and Dimension Reduction , 2011, Oper. Res..

[7]  Ken Seng Tan,et al.  An Accelerating Quasi-Monte Carlo Method for Option Pricing Under the Generalized Hyperbolic L[e-acute]vy Process , 2009, SIAM J. Sci. Comput..

[8]  Anargyros Papageorgiou,et al.  The Brownian Bridge Does Not Offer a Consistent Advantage in Quasi-Monte Carlo Integration , 2002, J. Complex..

[9]  Philipp Mayer,et al.  Introduction to Quantitative Methods for Financial Markets , 2013 .

[10]  J. Dick,et al.  A Discrepancy Bound for a Deterministic Acceptance-Rejection Sampler , 2013, 1307.1185.

[11]  Gunther Leobacher,et al.  Stratified sampling and quasi-Monte Carlo simulation of Lévy processes , 2006, Monte Carlo Methods Appl..

[12]  Klaus Scheicher,et al.  Complexity and effective dimension of discrete Lévy areas , 2007, J. Complex..

[13]  Ken Seng Tan,et al.  A general dimension reduction technique for derivative pricing , 2006 .

[14]  Pierre L'Ecuyer,et al.  Monte Carlo and Quasi-Monte Carlo Methods 2008 , 2009 .

[15]  E. Novak,et al.  Tractability of Multivariate Problems , 2008 .

[16]  Gunther Leobacher,et al.  Fast orthogonal transforms for pricing derivatives with quasi-Monte Carlo , 2012, Proceedings Title: Proceedings of the 2012 Winter Simulation Conference (WSC).

[17]  Benjamin J. Waterhouse,et al.  Fast Principal Components Analysis Method for Finance Problems With Unequal Time Steps , 2009 .

[18]  M. J. Wichura The percentage points of the normal distribution , 1988 .

[19]  A. Owen,et al.  Valuation of mortgage-backed securities using Brownian bridges to reduce effective dimension , 1997 .

[20]  Henryk Wozniakowski,et al.  Tractability of multivariate problems for standard and linear information in the worst case setting: Part I , 2015, J. Approx. Theory.

[21]  Wolfgang Hörmann,et al.  Automatic Nonuniform Random Variate Generation , 2011 .

[22]  Gunther Leobacher Fast orthogonal transforms and generation of Brownian paths , 2012, J. Complex..

[23]  Pierre-Louis Lions,et al.  Applications of Malliavin calculus to Monte Carlo methods in finance , 1999, Finance Stochastics.