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In finance, a price (premium) is paid or received for purchasing or selling options.This article discusses the calculation of this premium in general. For further detail, see: Mathematical finance § Derivatives pricing: the Q world for discussion of the mathematics; Financial engineering for the implementation; as well as Financial modeling § Quantitative finance generally.
In mathematical finance, a Monte Carlo option model uses Monte Carlo methods [Notes 1] to calculate the value of an option with multiple sources of uncertainty or with complicated features. [1] The first application to option pricing was by Phelim Boyle in 1977 (for European options ).
Haug, E. G (2007). "Option Pricing and Hedging from Theory to Practice". Derivatives: Models on Models. Wiley. ISBN 978-0-470-01322-9. The book gives a series of historical references supporting the theory that option traders use much more robust hedging and pricing principles than the Black, Scholes and Merton model. Triana, Pablo (2009).
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.
The most common option pricing model is the Black-Scholes model, though there are others, such as the binomial and Monte Carlo models. To use these models, ...
In finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options.Essentially, the model uses a "discrete-time" (lattice based) model of the varying price over time of the underlying financial instrument, addressing cases where the closed-form Black–Scholes formula is wanting, which in general does not exist for the BOPM.
Finite difference methods were first applied to option pricing by Eduardo Schwartz in 1977. [2] [3]: 180 In general, finite difference methods are used to price options by approximating the (continuous-time) differential equation that describes how an option price evolves over time by a set of (discrete-time) difference equations.
Option value (i.e.,. price) is estimated via a predictive formula such as Black-Scholes or using a numerical method such as the Binomial model. This price incorporates the expected probability of the option finishing " in-the-money ".