218872 Words876 Pages

Preface
This is a book about Monte Carlo methods from the perspective of ﬁnancial engineering. 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 techniques and renewed interest in some old techniques. This is also a book about ﬁnancial engineering from the perspective of Monte Carlo methods. One of the best ways to develop an understanding of a model of, say, the term structure of interest rates is to implement a simulation of the model; and ﬁnding ways to improve the eﬃciency of a simulation motivates a deeper investigation into properties of a model. My intended audience is a mix of graduate*…show more content…*

Students often come to a course in Monte Carlo with limited exposure to this material, and the implementation of a simulation becomes more meaningful if accompanied by an understanding of a model and its context. Moreover, it is precisely in model details that many of the most interesting simulation issues arise. If the ﬁrst three chapters deal with running a simulation, the next three deal with ways of running it better. Chapter 4 presents methods for increasing precision by reducing the variance of Monte Carlo estimates. Chapter 5 discusses the application of deterministic quasi-Monte Carlo methods for numerical integration. Chapter 6 addresses the problem of discretization error that results from simulating discrete-time approximations to continuous-time models. The last three chapters address topics speciﬁc to the application of Monte Carlo methods in ﬁnance. Chapter 7 covers methods for estimating price sensitivities or “Greeks.” Chapter 8 deals with the pricing of American options, which entails solving an optimal stopping problem within a simulation. Chapter 9 is an introduction to the use of Monte Carlo methods in risk management. It discusses the measurement of market risk and credit risk in ﬁnancial portfolios. The models and methods of this ﬁnal chapter are rather diﬀerent from vii those in the other chapters,

Students often come to a course in Monte Carlo with limited exposure to this material, and the implementation of a simulation becomes more meaningful if accompanied by an understanding of a model and its context. Moreover, it is precisely in model details that many of the most interesting simulation issues arise. If the ﬁrst three chapters deal with running a simulation, the next three deal with ways of running it better. Chapter 4 presents methods for increasing precision by reducing the variance of Monte Carlo estimates. Chapter 5 discusses the application of deterministic quasi-Monte Carlo methods for numerical integration. Chapter 6 addresses the problem of discretization error that results from simulating discrete-time approximations to continuous-time models. The last three chapters address topics speciﬁc to the application of Monte Carlo methods in ﬁnance. Chapter 7 covers methods for estimating price sensitivities or “Greeks.” Chapter 8 deals with the pricing of American options, which entails solving an optimal stopping problem within a simulation. Chapter 9 is an introduction to the use of Monte Carlo methods in risk management. It discusses the measurement of market risk and credit risk in ﬁnancial portfolios. The models and methods of this ﬁnal chapter are rather diﬀerent from vii those in the other chapters,

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