Search results
Results from the WOW.Com Content Network
The binomial pricing model traces the evolution of the option's key underlying variables in discrete-time. This is done by means of a binomial lattice (Tree), for a number of time steps between the valuation and expiration dates. Each node in the lattice represents a possible price of the underlying at a given point in time.
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. The discrete difference equations may then be solved iteratively to calculate a price for the option. [ 4]
The Black–Scholes / ˌblæk ˈʃoʊlz / [ 1] 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 ...
The simplest lattice model is the binomial options pricing model; the standard ("canonical") method is that proposed by Cox, Ross and Rubinstein (CRR) in 1979; see diagram for formulae. Over 20 other methods have been developed, [9] with each "derived under a variety of assumptions" as regards the development of the underlying's price. [4]
Monte Carlo methods for option pricing. 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 ).
See Asset pricing for a listing of the various models here. As regards (2), the implementation, the most common approaches are: Closed form, analytic models: the most basic of these are the Black–Scholes formula and the Black model. Lattice models (Trees): Binomial options pricing model; Trinomial tree; Monte Carlo methods for option pricing
Ho–Lee model. In financial mathematics, the Ho-Lee model is a short-rate model widely used in the pricing of bond options, swaptions and other interest rate derivatives, and in modeling future interest rates. [ 1]: 381 It was developed in 1986 by Thomas Ho [ 2] and Sang Bin Lee. [ 3]
Hull–White model. In financial mathematics, the Hull–White model is a model of future interest rates. In its most generic formulation, it belongs to the class of no-arbitrage models that are able to fit today's term structure of interest rates. It is relatively straightforward to translate the mathematical description of the evolution of ...