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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. Broadly speaking, the term may refer to a similar PDE that can be derived for a variety of options, or more generally, derivatives.

The Black–Scholes or Black–Scholes–Merton model is a mathematical model for the dynamics of a financial market containing derivative investment instruments. From the parabolic partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that t

In statistical mechanics and information theory, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of the position or velocity of a particle under the influence of drag forces and random forces, as in Brownian motion. The equation can be generalized to other observables as well. The Fokker–Planck equation h

Martingale pricing is a pricing approach based on the notions of martingale and risk neutrality. The martingale pricing approach is a cornerstone of modern quantitative finance and can be applied to a variety of derivatives contracts, e.g. options, futures, interest rate derivatives, credit derivatives, etc.

In finance, MIDAS (an acronym for Market Interpretation/Data Analysis System) is an approach to technical analysis initiated in 1995 by the physicist and technical analyst Paul Levine, PhD, and subsequently developed by Andrew Coles, PhD, and David Hawkins in a series of articles and the book MIDAS Technical Analysis: A VWAP Approach to Trading and Investing in Today's Markets. Latterly,

In mathematics, stochastic partial differential equations (SPDEs) are a generalization of partial differential equations via random force terms and coefficients, in the same way ordinary stochastic differential equations generalize ordinary differential equations.