Customer Reviews

Monte Carlo Methods in Financial Engineering (Stochastic Modelling and Applied Probability) (v. 53)

5 star:		(10)
4 star:		(3)
3 star:		(5)
2 star:		(2)
1 star:		(0)

 

 

This 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 Lévy 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 Carrière-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.

Monte Carlo simulations are extensively used not only in finance but also in network modeling, bioinformatics, radiation therapy planning, physics, and meteorology, to name a few. This book gives a good overview of how they are used in financial engineering, with particular emphasis on pricing American options and risk management. Aspiring financial engineers will find much that is helpful in the book, and after reading it should be able to apply the methodologies in the book in whatever financial institution they find themselves employed. The mathematics may be too formidable for a practical trader, but the book is targeted to readers who intend to work as financial engineers in a high-powered financial institution. Due to constraints of space, only the last two chapters will be reviewed here.

The next-to-last chapter discusses the difficult problem of pricing American options, which the author introduces as an `embedded optimization problem': the value of an American option is found by finding the optimal expected discounted payoff, in order to find the best time to exercise the option. When applying Monte Carlo simulation, the author restricts himself to options that can only be exercised at a finite, fixed set of opportunities, with a discrete Markov chain used to model the underlying process representing the discounted payoff from the exercise of the option at a particular time. This allows the use of dynamic programming, which the author does throughout the chapter, with the further simplification that the discounting is omitted. The author also shows how to find the optimal value by finding the best value within a parametric class, giving in the process a more tractable problem. This approach considers a parametric class of exercise regions or stopping rules. The author's discussion is somewhat too brief, but he does quote many references that the reader can easily consult.

Also discussed are random tree methods, which simulate paths of the underlying Markov chain, and which allow more control on the error as the computational effort increases. The random tree method gives two consistent estimators, one biased high and one biased low, with both converging to the true value, and attempts to find the solution to the full optimal stopping problem and estimate the true value of an American option. The author discusses briefly the numerical tests that support this method. Similar to this method are stochastic mesh methods, the difference being that stochastic mesh methods utilize information coming from all nodes in the next time step. These methods are given detailed treatment in this chapter, along with detailed discussion of their limitations and computational complexity. Regression-based methods, which estimate continuation values from simulated paths, are discussed within the framework of stochastic mesh. These methods allow the estimation of continuation values from simulated paths and consequently to price American options by Monte Carlo simulation.

Still another method that is discussed in this chapter is that of state-space partitioning, which, as the name implies, involves the partitioning of the state space of the underlying Markov chain. Monte Carlo simulation then allows the calculation of the transition probabilities and the averaged payoffs, and then these calculations are used to obtain estimates of the approximating value function. The author discusses the problems with this approach, these arising mostly in high-dimensional state spaces, as expected.

The last chapter will be of particular interest to risk managers, wherein the author applies Monte Carlo simulation to portfolio management. The measurement of market risk in his view boils down to finding a statistical model for describing the movements in individual sources of risk and correlations between multiple sources of risk, and in calculating the change in the value of the portfolio as the underlying sources of risk change. Most interesting in the discussion is the use of heavy-tailed probability distributions to model the changes in market prices and risks. A few methods for calculating VAR are discussed, which is then followed by how to use Monte Carlo simulation for estimating VAR. The author reminds the reader of the pitfalls in using probability distributions based on historical data for sampling price changes. A variance reduction technique based on the delta-gamma approximation is used to reduce the number of scenarios needed for portfolio revaluation. The author first treats the case where the risk factors are distributed according to multivariate normal distribution, and then latter the case where the distribution is heavy-tailed. The delta-gamma approximation captures some of the nonlinearity in a portfolio that contains options. This nonlinearity arises because of the dependence of the option on the price of the underlying asset. Keeping the quadratic terms in the Taylor expansion of the portfolio change yields the delta (first derivative) and gamma (second derivative) terms (the sensitivities). One then must find the distribution of a quadratic function of normal random variable, which the author does numerically via transform inversion. Particularly interesting in this discussion is the use of `exponential twisting' to obtain a dramatic reduction in variance. One then samples from the `twisted distribution' provided the `twisting parameter' is chosen intelligently. The author gives references, and discuses in slight detail, results that show the asymptotic optimality for this method.

The case for a heavy-tailed distribution if of course much more involved, since there are no moment generating functions for the quantities of interest. The author gets around this by using an `indirect' delta-gamma approximation, which involves expressing the quantities of interest in terms of a new random variable that is more convenient to work with. The author also discusses various methods for doing variance reduction in the heavy-tailed case, one of these methods again involving exponential twisting. The chapter ends with a discussion of credit risk. The main item of interest here is the calculation of the time of default, which the author discusses in terms of the default intensity and intensity-based modeling using a stochastic intensity to model the time to default.

I just got this book and start reading a few topics of interest like Risk Management. The book covers a lot of material in various financial products (heavy on interest rate products) and disciplines and does a fairly detailed job. It would have been great to have expanded the book to cover some areas more in depth (credit and operational risk), but otherwise this book is pretty comprehensive in terms of Monte Carlo applications. The book also has a nice appendix section that covers stochastic calculus and other topics. I took a course by Professor Glasserman at Columbia University ages ago and the book as well as the course delivers. This book is an excellent reference for any practitioner or academic alike (highly recommended). If you had to choose, I also think this book is better than the Peter Jaeckel's book on Monte Carlo. Enjoy...

Let me start by saying that I'm not a "quant." I am interested in the calculations that quants do, and in Monte Carlo techniques in general. As a result, I'm reviewing only about half of this book, the half on generally applicable Monte Carlo techniques, and skipping the finance-specific material that it alternates with.

As something of a novice to advanced Monte Carlo techniques, I find this book immensely useful. The chapter on "Generating Random Numbers" helps, even if the description of the basic uniform generators could be stronger. Given the uniform generator, its descriptions of generators for non-uniform distributions work well for me. The "Sample Path" material is where I came into this book, really, looking for more insight into generation Brownian bridges. The math certainly is not for the notation-shy, but suffices for the dedicated practitioner. The next few chapters on variance reduction, quasi-MC, discretization, and sensitivity analysis are all widely applicable - I don't have immediate use for the material, but now I know where to look when the need arises. The remaining two chapters cover specific financial applications, and I leave comment on them to other readers.

This book gave me what I wanted, and lots more besides. Much of what it offers really isn't for me, though - the financial instruments being analyzed border on abstract art. I also felt a little pain at having no background in stochastic calculus, but some determination and a willingness to skip over fine points got me through well enough. The successful reader has a working knowledge of basic calculus, linear algebra, and probability. That reader must have a real interest in MC techniques, and should care about the financial decision-making to which Glasserman applies those techniques - but, as I prove, even that isn't necessary for getting a lot of value from this text.

-- wiredweird

This is the best book I've read in the last year on mathematical finance. It is a tightly focussed text on Monte Carlo methods no more no less. So you won't find things like day count fracs because that's not what it's about.

Glasserman is a true expert on the topic. My highlight was the chapter on variance reduction where the vast amount of detailed knowledge taught me a lot, although I implement monte carlo pricing models on a day to day basis.

This book is exactly what I was looking for. It goes into the depth and detail of Monte-Carlo methods that other books either do not address at all, or only give a very superficial mention. For readers that are interested in really understanding Monte-Carlo and sophisticated analytical techniques from a very indepth standpoint, this book is for you.

Literally speaking, it is THE book on the practical application of Monte Carlo method in quant finance. What is amazing about this book is, though essentially it is a book without serious competitor, the author obviously spent much time and effort in its organization and presentation. For example, the discussion on the classical interest rate models from CIR to LIBOR market model is so neat and CONCISE.

I would like to give it a 6 star. I am looking forward to seeing an even better second edition, in which I wish that some important techniques such as revised cholesky factoring, quantization tree method, etc., will be included.

Very 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.

The book is just right for a reader who is looking for state-of-the-art techniques in Monte-Carlo methods in general. The fact that the book is specific to financial systems does not limit the usability of the book in the manner it is written. There are a lots of useful references one can get out of this book.
The book is for advanced readers in the sense that it requires rigorous mathematical ability to understand all the concepts. It is by no means for a novice reader and requires background in computational mathematics.

I must admit it is magnificently written book. Not just the main thematical issues but also appendix, where, compared to other similar publications, Girsanov theorem is thoroughly explained. All in all it's
a very useful book for everyone who has some basic information about stochastic processes and wants to learn something more about it or deepen their's knowledges. Well done.