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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.
(The binomial model is the simplest and most common lattice model.) The "dynamic assumptions of expected volatility and dividends", e.g. expected changes to dividend policy , as well as of forecast changes in interest rates [ 13 ] as consistent with today's term structure , may also be incorporated in a lattice model; although a finite ...
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.
Additionally, the stochastic process of the underlying(s) may be specified so as to exhibit jumps or mean reversion or both; this feature makes simulation the primary valuation method applicable to energy derivatives. [11] Further, some models even allow for (randomly) varying statistical (and other) parameters of the sources
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 ...
In finance, equity is an ownership interest in property that may be offset by debts or other liabilities. Equity is measured for accounting purposes by subtracting liabilities from the value of the assets owned. For example, if someone owns a car worth $24,000 and owes $10,000 on the loan used to buy the car, the difference of $14,000 is equity.
To use the lattice based approach, the analyst constructs a "tree" of short rates—a zeroeth step—consistent with today's yield curve and short rate (caplet) volatility, and where the final time step of the tree corresponds to the date of the underlying swap's maturity. Models commonly used here are Ho–Lee, Black-Derman-Toy and Hull-White.