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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.
As above, the PDE is expressed in a discretized form, using finite differences, and the evolution in the option price is then modelled using a lattice with corresponding dimensions: time runs from 0 to maturity; and price runs from 0 to a "high" value, such that the option is deeply in or out of the money. The option is then valued as follows: [5]
In finance, a bond option is an option to buy or sell a bond at a certain price on or before the option expiry date. [1] These instruments are typically traded OTC.. A European bond option is an option to buy or sell a bond at a certain date in future for a predetermined price.
Real options valuation, also often termed real options analysis, [1] (ROV or ROA) applies option valuation techniques to capital budgeting decisions. [2] A real option itself, is the right—but not the obligation—to undertake certain business initiatives, such as deferring, abandoning, expanding, staging, or contracting a capital investment project. [3]
John Hull and Alan White, "One factor interest rate models and the valuation of interest rate derivative securities," Journal of Financial and Quantitative Analysis, Vol 28, No 2, (June 1993) pp. 235–254. John Hull and Alan White, "Pricing interest-rate derivative securities", The Review of Financial Studies, Vol 3, No. 4 (1990) pp. 573–592.