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Numerical Methods and Optimization in Finance by Enrico Schumann, Dietmar Maringer, Manfred Gilli

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Chapter Five

Binomial Trees

Publisher Summary

Binomial trees serve as an intuitive approach to explain the logic behind option pricing models and also as a versatile computational technique. The binomial model assumes that, over a short period of time Δt, a financial asset's price S either rises by a small amount or goes down a small amount. The probability of an uptick is p, while a downtick occurs with probability 1 - p. Probabilities here are generally risk-neutral ones. A model for price movements may either be additive (i.e., absolute movements) or multiplicative (i.e., relative movements). “Additive” and “multiplicative” here refer to units of the observed price; computationally, taking logarithms can change a multiplicative model. There ...

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