Binomial options pricing model

Binomial options pricing model (BOPM) is a numerical method for option valuation

The binomial options pricing model (BOPM) is a numerical method used for valuing options. It addresses cases where the closed-form Black–Scholes formula is not applicable, making it a versatile tool in financial modeling. BOPM uses a discrete-time, lattice-based model to simulate the varying price over time of the underlying financial instrument.

The binomial model was first proposed by William Sharpe in 1978 and later formalized by Cox, Ross, and Rubinstein in 1979, as well as Rendleman and Bartter in the same year. These contributions have solidified the model's place in financial theory and practice.

For binomial trees applied to fixed income and interest rate derivatives, one can refer to the Lattice model (finance) section on Interest rate derivatives. This indicates the model's adaptability to various financial instruments beyond just options.

Example

Consider an option with an underlying asset priced at $100. Using the BOPM, the model might simulate the asset's price increasing to $110 or decreasing to $90 in one time period. By repeating this process across multiple periods, the model can estimate the option's fair value.

Understanding the BOPM is crucial for financial professionals who need to value options when the Black-Scholes formula is not applicable. This knowledge enables them to make informed decisions in complex financial markets.

Related concepts

Fama–French three-factor model

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Capital asset pricing model

Treynor-Black model combines active stock picking with a passive market portfolio

Greeks (finance)

Greeks measure sensitivity of option prices to underlying parameters

the Capital Asset Pricing Model (CAPM) says

CAPM formula: Expected return = Rf + β(Rm - Rf)

Straddle

Straddle strategy profits from large price movements in either direction

Arbitrage pricing theory

APT uses multiple systematic risk factors; CAPM uses a single market index

Educational content, not financial advice.

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