What is the 'Heston Model'

The Heston Model is a type of stochastic volatility model used by financial professionals to price options. It can be compared to the Black-Scholes option pricing model.

BREAKING DOWN 'Heston Model'

The Heston Model was developed by associate finance professor Steven Heston in 1993. It is an option pricing model that can be used for pricing options on various securities.

Stochastic Volatility and Smile Models

As a stochastic volatility model, the Heston Model uses statistical methods to calculate and forecast option pricing with the assumption that volatility is arbitrary. The assumption that volatility is arbitrary rather than constant is the key factor that makes stochastic volatility models unique. Other types of stochastic volatility models include the SABR model, the Chen model and the GARCH model.

The Heston Model is also a type of volatility smile model. "Smile" refers to the volatility smile, a graphical representation of several options with identical expiration dates that show increasing volatility as the options become more in-the-money or out-of-the-money. The smile model's name derives from the concave shape of the graph, which resembles a smile.

Heston Model Methodology

The Heston Model is a closed-form solution for pricing options that seeks to overcome some of the shortcomings presented in the Black-Scholes option pricing model. The Heston Model is a tool for advanced investors.

It is calculated from the following:

Heston Model versus Black-Scholes

The Black-Scholes model for option pricing was introduced in 1970 and served as one of the first models for helping investors derive a price associated with an option on a security. In general it helped to promote option investing as it created a model for analyzing the price of options on various securities. Overall, option pricing models are used by advanced investors to estimate and gauge the price of a particular option, trading on an underlying security in the financial marketplace. Options, just like their underlying security, will have prices that change throughout the trading day. Option pricing models seek to analyze and integrate the variables that cause fluctuation of option prices in order to identify the best option price for investment.

Both the Black-Scholes and Heston Model are based on underlying calculations that can be coded and programed through advanced Excel or other quantitative systems. The Black-Scholes model is calculated from the following:

Black-Scholes Formula (See also: Black-Scholes Model)

The Black-Scholes call option formula is calculated by multiplying the stock price by the cumulative standard normal probability distribution function. Thereafter, the net present value (NPV) of the strike price multiplied by the cumulative standard normal distribution is subtracted from the resulting value of the previous calculation. In mathematical notation, C = S*N(d1) - Ke^(-r*T)*N(d2). Conversely, the value of a put option could be calculated using the formula: P = Ke^(-r*T)*N(-d2) - S*N(-d1). In both formulas, S is the stock price, K is the strike price, r is the risk-free interest rate and T is the time to maturity. The formula for d1 is: (ln(S/K) + (r + (annualized volatility)^2 / 2)*T) / (annualized volatility * (T^(0.5))). The formula for d2 is: d1 - (annualized volatility)*(T^(0.5)).

The Heston Model is noteworthy because it seeks to provide for one of the main limitations of the Black-Scholes model which holds volatility constant. The use of stochastic variables in the Heston Model provides for the notion that volatility is not constant but arbitrary.

Both the basic Black-Scholes model and the Heston Model still only provide option pricing estimates for a European option, which is an option that can only be exercised on its expiration date. Various research and models have been studied for pricing American options through both Black-Scholes and the Heston Model. These variations provide estimates for options that can be exercised on any date leading up to the expiration date, as is the case for American options.

  1. Volatility Smile

    A u-shaped pattern that develops when an option’s implied volatility ...
  2. Stochastic Modeling

    A method of financial modeling in which one or more variables ...
  3. Option Pricing Theory

    An option pricing theory is any model or theory-based approach ...
  4. Black's Model

    Black's Model is a variation of the popular Black-Scholes options ...
  5. Model Risk

    Model risk occurs when a financial model used to measure a firm's ...
  6. Local Volatility

    A model used in quantitative finance to calculate the unpredictability ...
Related Articles
  1. Trading

    The Anatomy of Options

    Find out how you can use the "Greeks" to guide your options trading strategy and help balance your portfolio.
  2. Trading

    The "True" Cost Of Stock Options

    Perhaps the real cost of employee stock options is already accounted for in the expense of buyback programs.
  3. Small Business

    Calculating (Small) Company Credit Risk

    Determining creditworthiness of smaller and medium-sized corporations isn't as easy as for larger companies, but these tips can help.
  4. Trading

    Stock Options: What's Price Got To Do With It?

    A thorough understanding of risk is essential in options trading. So is knowing the factors that affect option price.
  5. Trading

    Triple Screen Trading System - Part 5

    Stochastics can be very effective as the second screen in this three-part system. Find out how to use this popular oscillator.
  1. What is the relationship between implied volatility and the volatility skew?

    Learn what the relationship is between implied volatility and the volatility skew, and see how implied volatility impacts ... Read Answer >>
  2. How does implied volatility impact the pricing of options?

    Learn about two specific volatility types associated with options and how implied volatility can impact the pricing of options. Read Answer >>
  3. Implied Volatility

    Implied volatility is an important concept in option trading. Learn how it is calculated using the Black-Scholes option pricing ... Read Answer >>
  4. What is the difference between fast and slow stochastics in technical analysis?

    The main difference between fast stochastics and slow stochastics can be summed up in one word: sensitivity. Read Answer >>
  5. Are there any risks involved in trading put options through a traditional broker?

    Explore put option trading and different put option strategies. Learn the difference between traditional, online and direct ... Read Answer >>
Hot Definitions
  1. Compound Annual Growth Rate - CAGR

    The Compound Annual Growth Rate (CAGR) is the mean annual growth rate of an investment over a specified period of time longer ...
  2. Net Present Value - NPV

    Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows ...
  3. Price-Earnings Ratio - P/E Ratio

    The Price-to-Earnings Ratio or P/E ratio is a ratio for valuing a company that measures its current share price relative ...
  4. Internal Rate of Return - IRR

    Internal Rate of Return (IRR) is a metric used in capital budgeting to estimate the profitability of potential investments.
  5. Limit Order

    An order placed with a brokerage to buy or sell a set number of shares at a specified price or better.
  6. Current Ratio

    The current ratio is a liquidity ratio that measures a company's ability to pay short-term and long-term obligations.
Trading Center