Lattice-Based Model

What Is a Lattice-Based Model?

A lattice-based model is utilized to value derivatives by utilizing a binomial tree to figure the different ways the price of an underlying asset, like a stock, could assume control over the derivative's life. A binomial tree plots out the potential values graphically that option prices can have throughout various time spans.

Instances of derivatives that can be priced involving lattice models incorporate equity options as well as futures contracts for commodities and currencies. The lattice model is especially fit to the pricing of employee stock options (ESO), which have a number of unique credits.

Understanding a Lattice-Based Model

Lattice-based models can consider expected changes in different boundaries like volatility over the life of the options. Volatility is a measure of how much an asset's price varies over a specific period. Accordingly, lattice models can give more accurate figures of option prices than the Black-Scholes model, which has been the standard mathematical model for pricing options contracts.

The lattice-based model's flexibility in consolidating expected volatility changes is especially valuable in certain conditions, for example, pricing employee options at beginning phase companies. Such companies might expect lower volatility in their stock prices in the future as their organizations mature. The assumption can be figured into a lattice model, empowering more accurate options pricing than the Black-Scholes model, which expects a similar level of volatility over the life of the option.

The binomial options pricing model (BOPM) is a lattice method for esteeming options. The initial step of the BOPM is to build the binomial tree. The BOPM is based on the underlying asset throughout some undefined time frame versus a single point in time. These models are called "lattice" in light of the fact that the different steps pictured in the model can have all the earmarks of being woven together like a lattice.

Special Considerations

A lattice model is just one type of model that is utilized to price derivatives. The name of the model is derived from the presence of the binomial tree that portrays the potential ways the derivative's price might take. The Black-Scholes is viewed as a shut structure model, which expects that the derivative is exercised toward the finish of its life.

For instance, the Black-Scholes model-while pricing stock options-expects that employees holding options lapsing in decade won't exercise them until the expiration date. The assumption is viewed as a weakness of the model since, in real life, option holders frequently exercise them a long time before they terminate.

Illustration of a Binomial Tree

Expect a stock has a price of $100, an option strike price of $100, a one-year expiration date, and an interest rate (r) of 5%.

Toward the year's end, there is a half likelihood the stock will rise to $125 and a half likelihood it will drop to $90. If the stock rises to $125 the value of the option will be $25 ($125 stock price minus $100 strike price) and assuming it drops to $90 the option will be worthless.

The option value will be:

Option value = [(probability of rise * up value) + (likelihood of drop * down value)]/(1 + r) = [(0.50 * $25) + (0.50 * $0)]/(1 + 0.05) = $11.90.

Features

• A lattice-based model is utilized to value derivatives, which are financial instruments that get their price from an underlying asset.
• Lattice-based models can consider expected changes in different boundaries like volatility during an option's life.
• Lattice models utilize binomial trees to show the various ways the price of an underlying asset could assume control over the derivative's life.