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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.
Lattice model (finance) Binomial Lattice for equity, with CRR formulae. Tree for an ( embedded) 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 finance, a lattice model [1] is a technique applied to the valuation of derivatives, where a discrete 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]
Trinomial tree. 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. It can also be shown that the approach is equivalent to the explicit finite difference method ...
In mathematical finance, the Black–Derman–Toy model ( BDT) is a popular short-rate model used in the pricing of bond options, swaptions and other interest rate derivatives; see Lattice model (finance) § Interest rate derivatives. It is a one-factor model; that is, a single stochastic factor—the short rate—determines the future ...
Cox–Ingersoll–Ross model. In mathematical finance, the Cox–Ingersoll–Ross (CIR) model describes the evolution of interest rates. It is a type of "one factor model" ( short-rate model) as it describes interest rate movements as driven by only one source of market risk. The model can be used in the valuation of interest rate derivatives.
Black–Scholes model. 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 ...
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 ).