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雷达卡
英文版，304页，国际主流金融工程教材。作者 Domingo Tavella, John Wiley & Sons出版。
The book is divided into seven chapters covering an introduction to
stochastic calculus, a summary of asset pricing theory, simulation applied
to pricing, and pricing using finite difference solutions. The topic of trees as
a tool for pricing is touched on at the end of the finite differences chapter.
Although trees are a popular pricing technique, finite differences, of which
trees are a particularly simple case, are a far more powerful and flexible
approach. Significant effort is dedicated to the fundamentals of early exercise
simulation. This methodology is rapidly taking the lead as a preferred
way to price highly dimensional early exercise instruments.
Chapter 1 is a brief introduction to single-period pricing with the
objective of motivating the idea that the price of a financial instrument is
given by an expectation.
Chapter 2 is a summary introduction to the basic elements of stochastic
calculus. The material is presented in a nonrigorous way and should be
easy to follow by anyone with a basic background in elementary calculus.
Chapter 3 is a brief description of pricing in continuous time, where
the main objectives are to more precisely determine the price as an expectation
under a suitable measure and to derive the relevant pricing equation.
Chapter 4 focuses on the generation of scenarios for simulation. In
practical implementations of simulation, the generation of scenarios of
appropriate quality is essential. Issues of accuracy are discussed in detail.
Chapter 5 is dedicated to simulation applied to computing expectations
for European pricing. This chapter gives a summary with selected case
studies of the main approaches that have demonstrated practical value in
financial pricing.
Chapter 6 deals with simulation applied to early exercise pricing. At
the time of this writing, this is a rapidly evolving subject. For this reason,
this chapter must be viewed as an update of the most established aspects of
simulation for early exercise pricing. The chapter presents a brief historical
account of the various techniques, but the emphasis is on linear squares
Monte Carlo, the technique that has marked a breakthrough in this area.
Chapter 7 summarizes the use of finite differences in option pricing.
The material is presented in a concise manner, with an emphasis on the fundamentals.
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