Release Date: 07 August, 2003
Hardcover
|
Book Description
Monte Carlo Methods are among the most broadly applicable and thus most powerful tools for valuing derivatives securities and measuring their risks. As computer speeds continue to increase and new research expands the scope and efficiency of these methods, their use is destined to grow. This book is devoted to the use of Monte Carlo methods in finance. Advances in Monte Carlo methods in financial engineering take place at the interface between academic research and industry practice. This book targets that interface developing theory closely tied to applications. It is roughly divided into three parts: the first three chapters concentrate on the basics of Monte Carlo methods; the next three develop ways to improve Monte Carlo methods; and the final four chapters deal with more specialized problems arising, in particular applications of Monte Carlo to financial engineering. This book will serve as a reference for practitioners and researchers and will also be suitable as a graduate text for courses on computational finance.
Book Info
Text develops the use of Monte Carlo methods in finance, and uses simulation as a vehicle for presenting models and ideas from financial engineering. For graduate students in financial engineering, researchers in Monte Carlo simulation, and practitioners in industry. DLC: Financial engineering. Rating 4.0
An accessible overview of Monte Carlo methods in financeThis new book, written by an active contributor to the field of Monte Carlo methods in finance, summarizes the ongoing interaction between theory and practice in a way that is readily accessible to graduate students and practitioners in quantitative finance.
The book is as self-contained as possible: basic notions on Monte Carlo simulation and option pricing are recalled in the first chapter and the second chapter explains how random number generators are designed. Chapter 3 explains how to generate sample paths for some commonly used stochastic models: multifactor Gaussian models, square root diffusions, diffusions with Poisson jumps, some examples of L?İvy processes and the LIBOR market model. Instead of giving a general result and leaving the reader on his own, the author treats each example with a fair amount of detail.
Chapter 4, which is the longest and probably the best chapter in the book, discusses variance reduction techniques. Variance reduction is what makes all the difference between a basic Monte Carlo simulation and a state-of-the-art algorithm incorporating the tricks of the trade. Apart from classical topics such as control variates, stratified sampling and importance sampling, the author (briefly) discusses more advanced topics such as the Weighted Monte Carlo method of Avellaneda et al., viewing it as a variance reduction method.
While computation of prices as expectations are standard applications of the Monte Carlo methods, two other issues in finance have turned out to be more challenging to solve using Monte Carlo simulation: the computation of sensitivities ("Greeks") and the pricing of American options, which involves the maximization of conditional expectations. Chapter 7 deals with the computation of sensitivities using finite differences, pathwise derivatives and the likelihood ratio method. More advanced methods based on integration by parts ("Malliavin calculus") are only briefly mentioned in the conclusion to this chapter.
Chapter 8 deals with the (Monte Carlo) pricing of American options, an evolving research topic in which Paul Glasserman has been an active contributor. The author has succeeded in summarizing in 60 pages a survey of various approaches: parametric methods, quantization methods, the (Broadie-Glasserman) stochastic mesh method, regression-based methods of Carriere-Longstaff-Schwartz and duality methods (Haugh-Kogan, Rogers). The presentation is somewhat biased towards the Broadie-Glasserman approach (which is understandable..), whereas the Carri??re-Longstaff-Schwartz regression method seems to be the most popular one among practitioners. One can regret the absence of a systematic comparison between these various methods in terms of numerical performance but the chapter explains their interrelations, at least from a theoretical point of view.
While most texts on Monte Carlo methods in finance have exclusively focused on option pricing, simulation of extreme events in view of VaR computation constitute another important application of Monte Carlo simulation. Chapter 9 deals with this topic and presents some importance sampling methods for simulating tail events, which turn out to be especially useful when simulating joint default events in credit risk models. A crash course on credit risk modeling is included in the chapter.
The book is not written in a theorem-proof format but using an explanatory approach which I found quite pleasant, with lots of examples illustrating the results. This format seems suitable for students of financial engineering; mathematicians looking for proofs of convergence should look elsewhere. The level of generality of the results is just right for applications in finance: the author has avoided the pitfall of considering a too general framework and has chosen to focus on examples of stochastic processes actually used in financial engineering, which makes the text more understandable. Also, various simulation methods are compared by actually doing the simulations instead of simply discussing asymptotic convergence rates. What is lacking is perhaps a more systematic reference to bibliography to indicate where proofs of various results are to be found, which could be useful for PhD students or researchers consulting this book.
One can always complain about topics which have been left out or lightly treated- weighted Monte Carlo, parallel computing, Malliavin calculus, quantization methods, point processes, LIBOR models with jumps,...-but the book is already 600 pages long and it seems retrospectively that it would have been difficult to include more material without greatly expanding the volume.
I have no doubt that this book will find many interested readers among quants and graduate students in quantitative finance and can even serve as an introduction to quantitative finance for non-specialist readers with a good quantitative background.Mathematically disappointing bookDon't be fooled by the name of the Springer series where this book appeared: if you are looking for a nice list of examples and applications, then this book may be ok, but otherwise, this is not the place to look for proofs and rigorous results.Excellent ReadVery well written book , all you need to know about MC Methods.
If you want to buy one book buy this one, if you have deep pockets then may be you should get the Peter Jaeckal book along with this. There is another introductory book on Simulation by Sheldon Ross. |
|
