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Lattice-Based Model

What is 'Lattice-Based Model'

An option pricing model that involves the construction of a binomial tree to show the different paths that the underlying asset may take over the option's life. A lattice model can take into account expected changes in various parameters such as volatility over the life of the options, providing more accurate estimates of option prices than the Black-Scholes model. The lattice model is particularly suited to the pricing of employee stock options, which have a number of unique attributes.

Explaining 'Lattice-Based Model'

The lattice model's flexibility in incorporating expected volatility changes is especially useful in certain circumstances, such as pricing employee options at early-stage companies. Such companies may expect lower volatility in their stock prices in the future as their businesses mature. This assumption can be factored into a lattice model, enabling more accurate option pricing than the Black-Scholes model, which inputs the same level of volatility over the life of the option.


Further Reading


A lattice-based model to evaluate variable annuities with guaranteed minimum withdrawal benefits under a regime-switching model
www.tandfonline.com [PDF]
… M. Costabile Department of Economics, Statistics and Finance, University of Calabria, Rende, Italy … The proposed model is based on a lattice that approximates the investment fund value … First, lattice-based models are effective tools when closed-form formulas are not available …

A comparison of lattice based option pricing models on the rate of convergenceA comparison of lattice based option pricing models on the rate of convergence
www.sciencedirect.com [PDF]
… M. Costabile Department of Economics, Statistics and Finance, University of Calabria, Rende, Italy … The proposed model is based on a lattice that approximates the investment fund value … First, lattice-based models are effective tools when closed-form formulas are not available …

American stochastic volatility call option pricing: A lattice based approachAmerican stochastic volatility call option pricing: A lattice based approach
link.springer.com [PDF]
… M. Costabile Department of Economics, Statistics and Finance, University of Calabria, Rende, Italy … The proposed model is based on a lattice that approximates the investment fund value … First, lattice-based models are effective tools when closed-form formulas are not available …

Structural default modeling: A lattice-based approachStructural default modeling: A lattice-based approach
jod.pm-research.com [PDF]
… M. Costabile Department of Economics, Statistics and Finance, University of Calabria, Rende, Italy … The proposed model is based on a lattice that approximates the investment fund value … First, lattice-based models are effective tools when closed-form formulas are not available …

A Lattice‐Based Method for Pricing Electricity Derivatives Under the Threshold ModelA Lattice‐Based Method for Pricing Electricity Derivatives Under the Threshold Model
www.tandfonline.com [PDF]
… M. Costabile Department of Economics, Statistics and Finance, University of Calabria, Rende, Italy … The proposed model is based on a lattice that approximates the investment fund value … First, lattice-based models are effective tools when closed-form formulas are not available …

Design and fabrication of periodic lattice-based cellular structuresDesign and fabrication of periodic lattice-based cellular structures
www.tandfonline.com [PDF]
… M. Costabile Department of Economics, Statistics and Finance, University of Calabria, Rende, Italy … The proposed model is based on a lattice that approximates the investment fund value … First, lattice-based models are effective tools when closed-form formulas are not available …

A new lattice-based scheme for swing option pricing under mean-reverting regime-switching jump-diffusion processesA new lattice-based scheme for swing option pricing under mean-reverting regime-switching jump-diffusion processes
www.sciencedirect.com [PDF]
… M. Costabile Department of Economics, Statistics and Finance, University of Calabria, Rende, Italy … The proposed model is based on a lattice that approximates the investment fund value … First, lattice-based models are effective tools when closed-form formulas are not available …

A non‐lattice pricing model of American options under stochastic volatilityA non‐lattice pricing model of American options under stochastic volatility
onlinelibrary.wiley.com [PDF]
… M. Costabile Department of Economics, Statistics and Finance, University of Calabria, Rende, Italy … The proposed model is based on a lattice that approximates the investment fund value … First, lattice-based models are effective tools when closed-form formulas are not available …

Lattice-based risk minimization training for unsupervised language model adaptationLattice-based risk minimization training for unsupervised language model adaptation
www.isca-speech.org [PDF]
… M. Costabile Department of Economics, Statistics and Finance, University of Calabria, Rende, Italy … The proposed model is based on a lattice that approximates the investment fund value … First, lattice-based models are effective tools when closed-form formulas are not available …



Q&A About Lattice-Based Model


Who uses lattice-based models?

Lattice-based models are used by employees who want to price employee stock options at early stage companies.

Why would you use a lattice based model for employee stock options at early stage companies?

Early stage companies may expect lower volatility in their stock prices in the future as their businesses mature. This assumption can be factored into a lattice based model, enabling more accurate option pricing than Black Scholes which inputs constant volatility over time.

What kind of exotic options can be valued using lattices?

Because of path dependence in the payout structure of exotic options, lattices are used for valuing certain exotic options.

How does a lattice-based model differ from other models?

The lattice-based model can take into account expected changes in various parameters such as volatility over the life of the options, providing more accurate estimates of option prices than other models.

How do lattices address issues with continuous models?

Lattices are additionally useful in that they address many of the issues encountered with continuous models such as pull to par.

What is a lattice model?

A lattice model is a technique applied to the valuation of derivatives, where a discrete time model is required. For equity options, a typical example would be pricing an American option, where a decision as to option exercise is required at all times (any time) before and including maturity. A continuous model, on the other hand, such as BlackScholes would only allow for the valuation of European options, where exercise is on the option's maturity date.

What is a lattice-based model?

A lattice-based model is an option pricing model that involves the construction of a binomial tree to show different paths that the underlying asset may take over the option's life.