The Heston model is an option pricing method that uses stochastic processes to model volatility and interest rates, taking into account variations in volatility observed in different options traded for the same asset. It was named after Steven L. Heston, who proposed the model in 1993. The model is one of the most used models based on stochastic volatility and is used to obtain trends in expected volatility observed in derivatives markets.
The Heston model is an option pricing method that takes into account the variations in volatility observed in different options traded at any given time for the same asset. It tries to recreate market prices using stochastic processes to model volatility and interest rates. The Heston model is characterized by the inclusion of the square root of a volatility function in the general pricing function.
The model was named for Steven L. Heston, a mathematical economist and business professor who holds a Ph.D. in finance from Carnegie Mellon and has held teaching positions at various universities, including Yale and Columbia. He proposed the model that was named after him in his 1993 article “A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options,” published in The Review of Financial Studies. The document examined the price of a European call option.
Options derive their values from the expected value of the gain that the option holder will be able to earn, which depends on the price and volatility of the underlying asset. A range of options with variable strike prices may be based on the same underlying asset. Theoretically, the volatility implied by each option price should be the same across all these options, because they are all based on the same asset. Some option pricing models, such as Black-Scholes, make this assumption and use an asset’s implied volatility to predict the option price at any strike price; others, like the Heston model, model volatility first and then draw conclusions about prices.
In practice, however, the volatility implied by an option price differs depending on the characteristics of the options, specifically the strike price. The central option is that with a strike price equal to the current market price of the underlying stock. This is also called the at-the-money option. As the strike price moves away from the market price, the volatility changes. Analysts create charts, called volatility bias charts, of this relationship, and name the charts, such as the volatility smile, according to their shapes.
Price models are supposed to predict the prices that products with certain characteristics will demand in the market. If the market returns different prices than the forecasts, the model must be updated. Stochastic volatility is a method of modeling variations in volatility. The Heston model is a way of modeling the price of an asset to obtain trends in expected volatility observed in derivatives markets using stochastic processes. It is one of the most used models based on stochastic volatility.
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