Derivatives: the theory and practice of financial engineering
Derivatives by Paul Wilmott provides the most comprehensive and accessible analysis of the art of science in financial modeling available. Wilmott explains and challenges many of the tried and tested models while at the same time offering the reader many new and previously unpublished ideas and techniques. Paul Wilmott has produced a compelling and essential new work in this field. The basics of the established theories-such as stochastic calculus, Black-Scholes, binomial trees and interest-rate models-are covered in clear and precise detail, but Derivatives goes much further. Complex models-such as path dependency, non-probabilistic models, static hedging and quasi-Monte Carlo methods-are introduced and explained to a highly sophisticated level. But theory in itself is not enough, an understanding of the role the techniques play in the daily world of finance is also examined through the use of spreadsheets, examples and the inclusion of Visual Basic programs. The book is divided into six parts: Part One: acts as an introduction and explanation of the fundamentals of derivatives theory and practice, dealing with the equity, commodity and currency worlds. Part Two: takes the mathematics of Part One to a more complex level, introducing the concept of path dependency. Part Three: concerns extensions of the Black-Scholes world, both classic and modern. Part Four: deals with models for fixed-income products. Part Five: describes models for risk management and measurement. Part Six: delivers the numerical methods required for implementing the models described in the rest of the book. Derivatives also includes a CD containing a wide variety of implementation material related to the book in the form of spreadsheets and executable programs together with resource material such as demonstration software and relevant contributed articles. At all times the style remains readable and compelling making Derivatives the essential book on every finance shelf.
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PART FOUR INTEREST RATES AND PRODUCTS
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American option amount arbitrage Asian option asset price asset value assume average barrier option binary call binomial Black-Scholes equation Black-Scholes value Black-Scholes world boundary conditions calculate cashflows Chapter constant contract correlation coupon crash delta hedging depends discrete dividend yield drift dt 2 dS2 early exercise example exercise price expected expiry final condition formulae forward rate gamma hedged portfolio implied volatility jump condition lognormal lookback market price maturity maximum nonlinear Normal distribution optimal option price option value parameters partial differential equation path-dependent quantity payment payoff position present value pricing equation probability density function problem put option put-call parity random walk rehedging risk-free rate risk-neutral satisfies shown in Figure simple solution solve spot interest rate spot rate standard deviation static hedging stochastic differential equation swap term timestep transaction costs underlying asset vanilla call volatility surface Wilmott worst-case yield curve zero zero-coupon bond