## What is the Heston Model?

The Heston Model, named after Steve Heston, is a type of stochastic volatility model used to price European options.

The Heston Model is an options pricing model that utilizes stochastic volatility.

This means that the model assumes that volatility is arbitrary, in contrast to the Black-Scholes model that holds volatility constant.

The Heston Model is a type of volatility smile model, which is a graphical representation of several options with identical expiration dates that show increasing volatility as the options become more ITM or OTM.

## Application of the Heston Model

Developed by mathematician Steven Heston in 1993, the Heston model was created to price options, which are a type of financial derivative. Unlike other financial assets such as equities, the value of an option is not based on the value of an asset but rather the change in an underlying asset’s price.

Each option is a contract between a buyer and seller, which gives the holder of the option the right to buy or sell the underlying asset at a specific price. All options have a specific expiration date, at which point the contract must be executed at the previously set price or risk expiring.

However, the volatility of options depends on the price and maturity. Therefore, the Heston model was designed to price an option while accounting for these variations in market volatility.

There are two categories of options: calls and puts. Calls allow the holder to buy at a specific price, and puts allow the holder to sell at a specific price.

Once a call or put option has been purchased, the date at which the holder can buy or sell depends on whether it is an American or European option. American options allow the holder to execute the option anytime before the expiry date, while European options only allow the holder to execute the option on the expiry date. It’s important to note that the Heston model is only capable of pricing European options.