Heston Stochastic Volatility Model for Option Pricing

Summary

The document introduces the Heston model as an option-pricing framework that allows both the underlying asset price and its variance to evolve stochastically. Unlike constant-volatility Black–Scholes, it models variance as mean reverting, with random fluctuations, and relates asset-price shocks to volatility shocks through a correlation parameter. The article explains the model’s main inputs, including initial price, mean-reversion speed and level, volatility of variance, correlation, rates, maturity, and strike. It connects stochastic volatility to the volatility smile observed across option strikes.

For European options, the described workflow defines parameters, evaluates a characteristic function, and derives an option price; the article also refers to numerical simulation and a Python implementation. It notes benefits for representing changing volatility, alongside limitations including calibration demands and weaker performance for short-dated options. The supplied text is incomplete in places, so it does not provide enough detail to reproduce the pricing procedure or assess the implementation. Extensions such as time-varying parameters and stochastic interest rates are mentioned, but their effects are not demonstrated with results.

Key ideas

• The Heston model represents volatility as a stochastic, mean-reverting process rather than a constant input.
• Its parameters describe volatility behavior, asset-volatility correlation, and contract characteristics.
• The model can capture a volatility smile that a constant-volatility framework does not represent directly.
• European option pricing is presented through parameter definition, characteristic-function calculation, and price evaluation.
• Calibration is required, and the document notes limitations for short-term options without providing comparative results.

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