What is the Heston model?

The Heston Model, named after Steve Heston, is a stochastic volatility model for pricing European options.

Learning the Heston Model

In 1993, associate finance professor Steven Heston created the Heston Model, a pricing model for options on various assets. The approach is similar to the popular Black-Scholes option pricing model.

Advanced investors use option pricing models to evaluate and gauge the price of an option trading on underlying securities in the financial market. Options prices move during the trading day, just like their underlying securities. Option pricing models examine and incorporate price fluctuations to get the optimum investment price.

As a stochastic volatility model, the Heston Model forecasts option prices using statistical methods, assuming arbitrary volatility. The premise that volatility is arbitrary, not constant, distinguishes stochastic volatility models. Additional stochastic volatility models include SABR, Chen, and GARCH.

Main Differences

• Features of the Steven Model separate it from other stochastic volatility models:
• There may be a link between the stock price and volatility.
• It shows volatility returning to its mean.
• It provides a closed-form solution using established mathematical methods.

A lognormal probability distribution for stock prices is not required.

Additionally, the Heston Model is a form of volatility smile model. The “Smile” image represents the volatility of options with similar expiry dates, indicating increased volatility as options grow more in-the-money (ITM) or out-of-the-money (OTM). Concave graphs resemble smiles; thus, they are the smile model’s name.

Methods of the Heston Model

The closed-form Heston Model for pricing options addresses some of the issues with the Black-Scholes model. The Steven Model helps advanced investors.

Black-Scholes vs. Heston Model

Since the 1970s, the Black-Scholes model has been a vital tool for investors to determine the value of an option on an asset. It devised a technique for assessing option prices on various assets, promoting option investment.

The Black-Scholes and Heston Models use sophisticated Excel or other quantitative tools to code and program their computations. Multiply the stock price by the cumulative standard normal probability distribution function to get the Black-Scholes call option formula.

After that, remove the strike price’s net present value (NPV) from the preceding computation using the cumulative standard normal distribution.

Special Considerations

This model addresses a significant drawback of the Black-Scholes model, which maintains volatility constants. Stochastic variables in the Heston Model indicate arbitrary volatility.

The basic Black-Scholes and Heston models only predict European option pricing on expiry. Price American options using Black-Scholes and the Steven Model. As with American options, these versions approximate options that can be exercised before expiration.

Conclusion

The Heston Model uses stochastic volatility to price options.

The model implies volatility is arbitrary, unlike the Black-Scholes model, which maintains volatility constant.

The volatility grin model, the Steven Model, depicts options with similar expiry dates with increased volatility as they grow more ITM or OTM.