Lattice-Based Model

A lattice-based model is used to value derivatives; it employs a binomial tree to show different paths the price of the underlying asset may take over the derivative's life. The name of the model is derived from the appearance of the binomial tree that depicts the possible paths the derivative's price may take. Derivatives that can be priced using lattice models include stock options and futures contracts on commodities and currencies, for example.

Lattice models 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.

The lattice-based 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 assumes the same level of volatility over the life of the option.

A lattice model is just one type of model that it used to price derivatives. Black-Scholes is considered a closed-form model. Closed-form models assume that the derivative is exercised at the end of its life. That is, in pricing stock options, for example, the Black-Scholes model assumes that if an employee has options that expire in 10 years, he/she will not exercise them until the expiration date. This is considered a weakness of this model since in real life owners of options are likely to exercise them well before they expire.