What is a Lattice-Based Model?

A lattice-based model is utilized for valuing derivatives; it makes use of a binomial tree to show various paths the underlying asset's price might take over the life of the derivative. The model's name is gotten from the appearance of the binomial tree which portrays the likely paths the price of the derivative may take. Derivatives which can be priced using lattice models comprise stock options, as well as, futures contracts on both currencies and commodities, for instance. Lattice models are capable of taking into account expected changes in different parameters like volatility over the options' life providing more precise estimates of option prices than the Black-Scholes model. The lattice model is specifically suited to the pricing of employee stock options, which have several unique attributes.

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How Does a Lattice-Based Model Work?

The flexibility of the lattice-based model in incorporating expected volatility changes is useful in specific situations, like pricing employee options at new companies. Companies such as these might expect lesser volatility in their future stock prices as their businesses mature. This supposition can be factored into a lattice model, enabling more precise option pricing than the Black-Scholes model, which has the same volatility level over an option's life. A lattice is only a model type which is utilized in pricing derivatives. Black-Scholes is termed a closed-form model. Closed-form models believe that the derivative is exercised at its life's end. This means that, in pricing stock options, for instance, the Black-Scholes model assumes that supposing an employee has options which have an expiration of 10 years, he/she wouldn't exercise them until the expiry date. This is termed a weakness of the model based on the fact that in reality, options owners tend to exercise them very well before their expiration.