Monte Carlo Methods in Financial Engineering (Stochastic Modelling and Applied Probability) | 
 enlarge | Author: Paul Glasserman
Publisher: Springer
Category: Book
List Price: $69.95
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Rating:  20 reviews
Sales Rank: 159145
Media: Hardcover
Edition: 1
Pages: 602
Number Of Items: 1
Shipping Weight (lbs): 2.5
Dimensions (in): 9.3 x 6.2 x 1.6
ISBN: 0387004513
Dewey Decimal Number: 658.15501519282
EAN: 9780387004518
Publication Date: August 7, 2003
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Product Description
Monte Carlo simulation has become an essential tool in the pricing of derivative securities and in risk management. These applications have, in turn, stimulated research into new Monte Carlo methods and renewed interest in some older techniques. This book develops the use of Monte Carlo methods in finance and it also uses simulation as a vehicle for presenting models and ideas from financial engineering. It divides roughly into three parts. The first part develops the fundamentals of Monte Carlo methods, the foundations of derivatives pricing, and the implementation of several of the most important models used in financial engineering. The next part describes techniques for improving simulation accuracy and efficiency. The final third of the book addresses special topics: estimating price sensitivities, valuing American options, and measuring market risk and credit risk in financial portfolios. The most important prerequisite is familiarity with the mathematical tools used to specify and analyze continuous-time models in finance, in particular the key ideas of stochastic calculus. Prior exposure to the basic principles of option pricing is useful but not essential. The book is aimed at graduate students in financial engineering, researchers in Monte Carlo simulation, and practitioners implementing models in industry. Mathematical Reviews, 2004: "... this book is very comprehensive, up-to-date and useful tool for those who are interested in implementing Monte Carlo methods in a financial context."
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| Customer Reviews: Read 15 more reviews...
 An excellent overview July 8, 2005
Dr. Lee D. Carlson (Saint Louis, Missouri USA)
24 out of 28 found this review helpful
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.
Monte Carlo applications and much more! November 5, 2003
T. Kim (Princeton, NJ United States)
14 out of 16 found this review helpful
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...
Excellent Read June 24, 2004
9 out of 10 found this review helpful
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.
a great buy January 15, 2004
10 out of 12 found this review helpful
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.
A wonderful book July 21, 2005
Z. Zheng
6 out of 8 found this review helpful
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.
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