Calibrating Heston Volatility Dynamics from Stock Price Paths

Summary

The document asks whether Heston stochastic volatility parameters can be estimated from the observed trajectory of the underlying stock, rather than calibrated from European call option prices. The author notes that the standard approach they encountered fits the model’s semi-closed-form option values to market prices, and wonders whether the stock dynamics implied by Heston could provide another source of parameter information.

No calibration procedure, comparison, or empirical evidence is provided; the post is an open question seeking references and discussion. The distinction matters because historical stock paths describe realized, physical dynamics, while option prices reflect risk-neutral pricing and market expectations. Estimating parameters from stock data may therefore answer a different question from fitting the model to option prices, and the document does not address how to reconcile those objectives or handle the model’s latent volatility.

Key ideas

• The post considers estimating Heston parameters from underlying stock price trajectories.
• It contrasts this idea with fitting model prices to traded European call options.
• Stock paths and option prices provide different information about the model’s dynamics and pricing measure.
• The document offers no method or empirical findings and seeks references and discussion.

Tags

# Can you calibrate the Heston model using stock price trajectories?


# Can you calibrate the Heston model using stock price trajectories?












I'm interested in calibrating the Heston model so I was reading about it online. All procedures I could find was using market prices for European call options and using the (semi-)closed-form expression to obtain parameters that would've yielded these call option prices.

However, the Heston dynamics tell us something about how the stock price behaves. Wouldn't it make more sense to use the stock price trajectory and infer reasonable parameters based on that information? I could not find anything similar in the literature but maybe I haven't searched thoroughly enough yet.

Does anyone know anything about this or has even tried it? I'm interested to hear your thoughts.

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