Finite Difference Models
The equations used to model the option are often expressed as partial differential equations (see for example Black–Scholes equation). Once expressed in this form, a finite difference model can be derived, and the valuation obtained. A number of implementations of finite difference methods exist for option valuation, including: explicit finite difference, implicit finite difference and the Crank-Nicholson method. A trinomial tree option pricing model can be shown to be a simplified application of the explicit finite difference method. Although the finite difference approach is mathematically sophisticated, it is particularly useful where changes are assumed over time in model inputs – for example dividend yield, risk free rate, or volatility, or some combination of these – that are not tractable in closed form.
Read more about this topic: Option (finance), Model Implementation
Famous quotes containing the words finite, difference and/or models:
“For it is only the finite that has wrought and suffered; the infinite lies stretched in smiling repose.”
—Ralph Waldo Emerson (1803–1882)
“The difference between humans and wild animals is that humans pray before they commit murder.”
—Friedrich Dürrenmatt (1921–1990)
“French rhetorical models are too narrow for the English tradition. Most pernicious of French imports is the notion that there is no person behind a text. Is there anything more affected, aggressive, and relentlessly concrete than a Parisan intellectual behind his/her turgid text? The Parisian is a provincial when he pretends to speak for the universe.”
—Camille Paglia (b. 1947)