Approaches to Calibrating the Heston Stochastic Volatility Model

Summary

The document surveys three approaches for calibrating the Heston stochastic volatility model. A price- or implied-volatility-based loss function minimizes discrepancies between observed option quotes and model outputs. Differential evolution searches the parameter space and is described as effective at finding a global minimum, though computationally expensive. Maximum likelihood estimation is presented as a method for estimating physical model parameters from historical stock-price time series.

The cited works are offered as entry points, rather than as a detailed implementation guide or a single recommended calibration procedure. The approaches target different data and objectives: market option prices or implied volatilities for loss-function calibration, broad numerical optimization for differential evolution, and historical time-series likelihood for maximum likelihood. The brief answer does not compare calibration accuracy, discuss parameter constraints or data quality, or explain how to validate a fitted model, so those choices require further study.

Key ideas

• Calibration can minimize errors between quoted option prices or implied volatilities and model values.
• Differential evolution can search for a global minimum but may require substantial computation.
• Maximum likelihood estimation can fit physical Heston parameters using historical stock-price data.
• Calibration method choice depends on the available data and the parameter-estimation objective.

Tags

# What is a canonical reference on calibrating the Heston Model?


# What is a canonical reference on calibrating the Heston Model?












I am trying to calibrate the Heston model (or another stochastic volatility model).

I read about maximum likelihood estimates, but there are so many articles as well with other algorithms.

Can you suggest an article (from https://papers.ssrn.com/) which explains a relatively easy algorithm that is applied nowadays.

## Answer by user16651 (score 4)

https://quant.stackexchange.com/a/30886

There are so many articles in this context, such as

- Estimating using loss function This method uses the error between quoted market prices and model prices, or between market and model implied volatilities . You can consider these article Heston’s Stochastic Volatility Model: Implementation,Calibration, and Some Extensions. Loss Functions in Option Valuation: A Framework for Selection. Empirical Performance of Alternative Option Pricing Models.

2.Differential evolution

Vollrath has applied the algorithm to interest rate and option model and has found the algorithm effective in identifying the global minimum in the parameter space, albeit at the expense of high computation time. You can this method in this article

- Calibration of Interest Rate and Option Models Using Differential Evolution.

3.Maximum likelihood estimation

Atiya and Wall (2009) show how to obtain the maximum likelihood estimates of the physical parameters of the Heston model using a time series of historical stock prices.

- An Analytic Approximation of the Likelihood Function for the Heston Model Volatility Estimation Problem.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.