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  2. Black–Scholes equation - Wikipedia

    en.wikipedia.org/wiki/BlackScholes_equation

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

  3. Black–Scholes model - Wikipedia

    en.wikipedia.org/wiki/BlackScholes_model

    In fact, the Black–Scholes 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 the two terms in the Black–Scholes formula.

  4. Finite difference methods for option pricing - Wikipedia

    en.wikipedia.org/wiki/Finite_difference_methods...

    The discrete difference equations may then be solved iteratively to calculate a price for the option. [4] The approach arises since the evolution of the option value can be modelled via a partial differential equation (PDE), as a function of (at least) time and price of underlying; see for example the Black–Scholes PDE. Once in this form, a ...

  5. Black model - Wikipedia

    en.wikipedia.org/wiki/Black_model

    The Black model (sometimes known as the Black-76 model) is a variant of the Black–Scholes option pricing model. Its primary applications are for pricing options on future contracts, bond options, interest rate cap and floors, and swaptions. It was first presented in a paper written by Fischer Black in 1976.

  6. Black's approximation - Wikipedia

    en.wikipedia.org/wiki/Black's_approximation

    In finance, Black's approximation is an approximate method for computing the value of an American call option on a stock paying a single dividend. It was described by Fischer Black in 1975. [1] The Black–Scholes formula (hereinafter, "BS Formula") provides an explicit equation for the value of a call option on a non-dividend paying stock. In ...

  7. Implied volatility - Wikipedia

    en.wikipedia.org/wiki/Implied_volatility

    The risk-free interest rate is 5%. XYZ stock is currently trading at $51.25 and the current market price of is $2.00. Using a standard Black–Scholes pricing model, the volatility implied by the market price is 18.7%, or:

  8. Girsanov theorem - Wikipedia

    en.wikipedia.org/wiki/Girsanov_theorem

    This theorem can be used to show in the Black–Scholes model the unique risk-neutral measure, i.e. the measure in which the fair value of a derivative is the discounted expected value, Q, is specified by

  9. Foreign exchange option - Wikipedia

    en.wikipedia.org/wiki/Foreign_exchange_option

    As in the Black–Scholes model for stock options and the Black model for certain interest rate options, the value of a European option on an FX rate is typically calculated by assuming that the rate follows a log-normal process. [3] The earliest currency options pricing model was published by Biger and Hull, (Financial Management, spring 1983).

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