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  2. Black–Scholes model - Wikipedia

    en.wikipedia.org/wiki/BlackScholes_model

    The BlackScholes model assumes positive underlying prices; if the underlying has a negative price, the model does not work directly. [ 51 ] [ 52 ] When dealing with options whose underlying can go negative, practitioners may use a different model such as the Bachelier model [ 52 ] [ 53 ] or simply add a constant offset to the prices.

  3. Black–Scholes equation - Wikipedia

    en.wikipedia.org/wiki/BlackScholes_equation

    In mathematical finance, the BlackScholes equation, also called the BlackScholes–Merton equation, is a partial differential equation (PDE) governing the price evolution of derivatives under the BlackScholes model. [1]

  4. Greeks (finance) - Wikipedia

    en.wikipedia.org/wiki/Greeks_(finance)

    The Greeks in the BlackScholes model (a relatively simple idealised model of certain financial markets) are relatively easy to calculate — a desirable property of financial models — and are very useful for derivatives traders, especially those who seek to hedge their portfolios from adverse changes in market conditions. For this reason ...

  5. Geometric Brownian motion - Wikipedia

    en.wikipedia.org/wiki/Geometric_Brownian_motion

    Geometric Brownian motion is used to model stock prices in the BlackScholes model and is the most widely used model of stock price behavior. [4] Some of the arguments for using GBM to model stock prices are: The expected returns of GBM are independent of the value of the process (stock price), which agrees with what we would expect in ...

  6. Option (finance) - Wikipedia

    en.wikipedia.org/wiki/Option_(finance)

    The most basic model is the BlackScholes model. More sophisticated models are used to model the volatility smile. These models are implemented using a variety of numerical techniques. [18] In general, standard option valuation models depend on the following factors: The current market price of the underlying security

  7. Itô's lemma - Wikipedia

    en.wikipedia.org/wiki/Itô's_lemma

    Itô's lemma can be used to derive the BlackScholes equation for an option. [2] Suppose a stock price follows a geometric Brownian motion given by the stochastic differential equation dS = S(σdB + μ dt). Then, if the value of an option at time t is f(t, S t), Itô's lemma gives

  8. Binary option - Wikipedia

    en.wikipedia.org/wiki/Binary_option

    In the BlackScholes model, the price of the option can be found by the formulas below. [27] In fact, the BlackScholes formula for the price of a vanilla call option (or put option) can be interpreted by decomposing a call option into an asset-or-nothing call option minus a cash-or-nothing call option, and similarly for a put – the binary options are easier to analyze, and correspond to ...

  9. Stochastic volatility - Wikipedia

    en.wikipedia.org/wiki/Stochastic_volatility

    This basic model with constant volatility is the starting point for non-stochastic volatility models such as BlackScholes model and Cox–Ross–Rubinstein model. For a stochastic volatility model, replace the constant volatility σ {\displaystyle \sigma } with a function ν t {\displaystyle \nu _{t}} that models the variance of S t ...