Black Scholes and Beyond: Option Pricing Models
McGraw-Hill Companies,Incorporated, 1997 - 496 páginas
An unprecedented book on option pricing! For the first time, the basics on modern option pricing are explained ``from scratch'' using only minimal mathematics. Market practitioners and students alike will learn how and why the Black-Scholes equation works, and what other new methods have been developed that build on the success of Black-Shcoles. The Cox-Ross-Rubinstein binomial trees are discussed, as well as two recent theories of option pricing: the Derman-Kani theory on implied volatility trees and Mark Rubinstein's implied binomial trees. Black-Scholes and Beyond will not only help the reader gain a solid understanding of the Balck-Scholes formula, but will also bring the reader up to date by detailing current theoretical developments from Wall Street. Furthermore, the author expands upon existing research and adds his own new approaches to modern option pricing theory. Among the topics covered in Black-Scholes and Beyond: detailed discussions of pricing and hedging options; volatility smiles and how to price options ``in the presence of the smile''; complete explanation on pricing barrier options.
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THE VOLATILITY SMILE
FUNDAMENTAL MATHEMATICAL CONCEPTS
THE GEOMETRIC BROWNIAN MOTION MODEL OF PRICE MOVE
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American option approximate arbitrage argument Arrow-Debreu price asset assume assumption barrier options binomial model binomial tree Black-Scholes formula Brownian motion model casino Chapter compounded compute cost of hedging Cox-Ross-Rubinstein cumulative normal distribution delta discuss displays dividend payments equal equation European call option European option ex-dividend date example expected return expected value Figure flip forward contract forward price geometric Brownian motion graph hedge parameters hedging strategy implied volatility trees input interest rate investment investor mean method move number of periods one-period option expires option pricing option value tree outcomes path payout percent put option put-call parity random event random variable rate of interest rate of return ratio rebalancing represents risk risk-free rate riskless Scholes self-financing sell shares short position spot price standard deviation step stock index stock price model stock price movements stock price tree stock returns strike price Suppose theta tion transition probability vega volatility smile zero
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