Book•
Monte Carlo Methods in Financial Engineering
07 Aug 2003-
TL;DR: This paper presents a meta-modelling procedure that automates the very labor-intensive and therefore time-heavy and therefore expensive and expensive process of manually computing random numbers and random Variables.
Abstract: Foundations.- Generating Random Numbers and Random Variables.- Generating Sample Paths.- Variance Reduction Techniques.- Quasi-Monte Carlo Methods.- Discretization Methods.- Estimating Sensitivities.- Pricing American Options.- Applications in Risk Management.- Appendices
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TL;DR: It is shown that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations.
Abstract: We show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In the simplest case of a Lipschitz payoff and a Euler discretisation, the computational cost to achieve an accuracy of O(e) is reduced from O(e-3) to O(e-2 (log e)2). The analysis is supported by numerical results showing significant computational savings.
1,619 citations
Cites methods from "Monte Carlo Methods in Financial En..."
...This calculation of an optimal number of samples Nl is similar to the approach used in optimal stratified sampling (Glasserman 2004), except that in this case we also include the effect of the different computational cost of the samples on different levels....
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...The multilevel method is very easy to implement and can be combined, in principle, with other variance reduction methods such as stratified sampling (Glasserman 2004) and quasi-Monte Carlo methods (Kuo and Sloan 2005, L’Ecuyer 2004, Niederreiter 1992) to obtain even greater savings....
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...Current research is investigating how to achieve a similar improvement in the convergence rate for lookback, barrier, and digital options, based on the appropriate use of Brownian interpolation (Glasserman 2004), as well as the extension to multidimensional SDEs....
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TL;DR: This work provides an introduction to variational autoencoders and some important extensions, which provide a principled framework for learning deep latent-variable models and corresponding inference models.
Abstract: Variational autoencoders provide a principled framework for learning deep latent-variable models and corresponding inference models. In this work, we provide an introduction to variational autoencoders and some important extensions.
1,089 citations
Cites background from "Monte Carlo Methods in Financial En..."
..., 2012), often in combination with various novel control variate techniques (Glasserman, 2013) for variance reduction....
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TL;DR: In this article, a security-constrained unit commitment (SCUC) algorithm is proposed for managing the security of power system operation by taking into account the intermittency and volatility of wind power generation.
Abstract: This paper presents a security-constrained unit commitment (SCUC) algorithm which takes into account the intermittency and volatility of wind power generation. The UC problem is solved in the master problem with the forecasted intermittent wind power generation. Next, possible scenarios are simulated for representing the wind power volatility. The initial dispatch is checked in the subproblem and generation redispatch is considered for satisfying the hourly volatility of wind power in simulated scenarios. If the redispatch fails to mitigate violations, Benders cuts are created and added to the master problem to revise the commitment solution. The iterative process between the commitment problem and the feasibility check subproblem will continue until simulated wind power scenarios can be accommodated by redispatch. Numerical simulations indicate the effectiveness of the proposed SCUC algorithm for managing the security of power system operation by taking into account the intermittency and volatility of wind power generation.
869 citations
Cites methods from "Monte Carlo Methods in Financial En..."
...The idea in applying LHS is to distribute each sample as the only one in each axis-aligned hyperplane [13]....
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Book•
15 Mar 2011
TL;DR: Handbook of Monte Carlo Methods is an excellent reference for applied statisticians and practitioners working in the fields of engineering and finance who use or would like to learn how to use Monte Carlo in their research.
Abstract: A comprehensive overview of Monte Carlo simulation that explores the latest topics, techniques, and real-world applications
More and more of today’s numerical problems found in engineering and finance are solved through Monte Carlo methods. The heightened popularity of these methods and their continuing development makes it important for researchers to have a comprehensive understanding of the Monte Carlo approach. Handbook of Monte Carlo Methods provides the theory, algorithms, and applications that helps provide a thorough understanding of the emerging dynamics of this rapidly-growing field.
The authors begin with a discussion of fundamentals such as how to generate random numbers on a computer. Subsequent chapters discuss key Monte Carlo topics and methods, including:
- Random variable and stochastic process generation
- Markov chain Monte Carlo, featuring key algorithms such as the Metropolis-Hastings method, the Gibbs sampler, and hit-and-run
- Discrete-event simulation
- Techniques for the statistical analysis of simulation data including the delta method, steady-state estimation, and kernel density estimation
- Variance reduction, including importance sampling, latin hypercube sampling, and conditional Monte Carlo
- Estimation of derivatives and sensitivity analysis
- Advanced topics including cross-entropy, rare events, kernel density estimation, quasi Monte Carlo, particle systems, and randomized optimization
The presented theoretical concepts are illustrated with worked examples that use MATLAB, a related Web site houses the MATLAB code, allowing readers to work hands-on with the material and also features the author's own lecture notes on Monte Carlo methods. Detailed appendices provide background material on probability theory, stochastic processes, and mathematical statistics as well as the key optimization concepts and techniques that are relevant to Monte Carlo simulation.
Handbook of Monte Carlo Methods is an excellent reference for applied statisticians and practitioners working in the fields of engineering and finance who use or would like to learn how to use Monte Carlo in their research. It is also a suitable supplement for courses on Monte Carlo methods and computational statistics at the upper-undergraduate and graduate levels.
840 citations
TL;DR: This article reviewed the term structure of interest rates literature relating to the arbitrage-free pricing and hedging of interest rate derivatives and emphasized term structure theory, including the HJM model, forward and futures contracts, the expectations hypothesis, and pricing of caps/floors.
638 citations