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Binomial Lattice for equity, with CRR formulae Tree for an bond option returning the OAS (black vs red): the short rate is the top value; the development of the bond value shows pull-to-par clearly . In quantitative finance, a lattice model [1] is a numerical approach to the valuation of derivatives in situations requiring a discrete time model.
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 [1].
The trinomial tree is a lattice-based computational model used in financial mathematics to price options.It was developed by Phelim Boyle in 1986. It is an extension of the binomial options pricing model, and is conceptually similar.
Using the calibrated lattice one can then value a variety of more complex interest-rate sensitive securities and interest rate derivatives. Although initially developed for a lattice-based environment, the model has been shown to imply the following continuous stochastic differential equation: [1] [5]
It is relatively straightforward to translate the mathematical description of the evolution of future interest rates onto a tree or lattice and so interest rate derivatives such as bermudan swaptions can be valued in the model. The first Hull–White model was described by John C. Hull and Alan White in 1990. The model is still popular in the ...
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 ).
Lattice model may refer to: Lattice model (physics), a physical model that is defined on a periodic structure with a repeating elemental unit pattern, as opposed to the continuum of space or spacetime; Lattice model (finance), a "discrete-time" model of the varying price over time of the underlying financial instrument, during the life of the ...
Physical lattice models frequently occur as an approximation to a continuum theory, either to give an ultraviolet cutoff to the theory to prevent divergences or to perform numerical computations. An example of a continuum theory that is widely studied by lattice models is the QCD lattice model, a discretization of quantum chromodynamics.