Joint Maximum and Terminal Returns in the Heston Model

Summary

The document poses a stochastic-modeling question about the Heston model. It asks for the joint probability distribution of two quantities over a time interval: the maximum return reached between the initial time and the endpoint, and the return at that endpoint. The specified setting has zero return drift and nonzero correlation between the equity and variance factors.

No proposed distribution, derivation, numerical method, or answer is included. As a result, the text identifies a quantitative finance problem rather than teaching a solution. The nonzero correlation condition is central to the question, since it rules out simply treating the equity and variance factors as independent. The document also does not specify conventions for returns, initial variance, parameter values, or boundary treatment, so those details would need to be fixed before a concrete distribution or computational approach could be assessed.

Key ideas

• The question concerns the Heston stochastic volatility model.
• It asks for the joint law of the path maximum return and the return at the endpoint.
• The stated setting assumes zero return drift and nonzero equity-variance correlation.
• No distribution, derivation, or computational method is supplied.

Tags

# Heston Model Maximum Return Distribution


# Heston Model Maximum Return Distribution












What is the joint probability distribution of the maximum of the return between time $0$ and $t$ and the return at $t$, for the Heston model, when the return drift is $0$ and the correlation between the equity factor and the variance factor is nonzero?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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