Black Scholes and Beyond: Option Pricing Models
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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STOCKS OPTIONS AND FUTURES
FUNDAMENTAL MATHEMATICAL CONCEPTS
THE GEOMETRIC BROWNIAN MOTION MODEL OF PRICE MOVE
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120 Stock price American option Arrow-Debreu price assume assumption backward induction barrier options binomial model Black-Scholes formula Black-Scholes price Brownian motion model Chapter compute the value correlated cost of hedging Cox-Ross-Rubinstein delta discuss displays dividend payments equal equation European call option European options ex-dividend date example expected value Figure forward price geometric Brownian motion given graph hedge parameters hedging portfolio hedging strategy implied binomial trees implied tree implied volatility trees input interest rate knock-in local volatility market price means method move normal distribution number of periods one-period option expires option pricing option value tree path price options put option random variable rate of interest rate of return ratio rebalancing represents risk risk-free rate riskless Rubinstein Scholes spot price standard binomial tree standard deviation step stochastic volatility stock price movements stock price tree strike price terminal nodes theta tree model underlying up-transition probability value of node vega volatility smile zero
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