Pricing European Calls with the Heston Model and Full Truncation Euler

Summary

The article extends constant-volatility option pricing with the Heston model, in which asset returns and variance evolve stochastically and their driving processes are correlated. It explains the variance process’s long-run level, mean-reversion rate, volatility of variance, and correlation with the asset path. Because both paths must be simulated numerically, it uses Euler discretization and applies full truncation to keep negative variance approximations from affecting subsequent calculations.

For a European call, Monte Carlo simulation generates correlated normal draws, evolves variance and asset paths, averages terminal payoffs, and discounts at the risk-free rate. The implementation is modular, with separate option payoff, distribution, correlation, and path-generation components. One reported price is compared with a reference exact price; the article says more simulations and finer time steps can improve accuracy. Results remain subject to discretization and sampling error, and calibration to market data and time-varying parameters are left for future work.

Key ideas

• The Heston model adds a stochastic, mean-reverting variance process correlated with asset returns.
• Full truncation Euler uses nonnegative variance in the variance update terms to handle discretization errors.
• Correlated normal draws drive the simulated asset and variance paths.
• Monte Carlo pricing averages terminal call payoffs and discounts the mean at the risk-free rate.
• The reported estimate can be affected by simulation count and discretization, while market calibration is outside the article’s scope.

Tags

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