Choosing Volatility Inputs When Inferring Implied Correlation

Summary

The document raises an input-selection problem in estimating implied correlation from bivariate option prices. The described approach trains a model on a decade of returns, prices options, and inverts Stulz's formula to infer a correlation coefficient. Because the formula also requires each asset's volatility, the author asks whether implied volatility or historical volatility is appropriate when those measures move on a different timescale from the model's prices.

The passage supplies no proposed alternative, answer, results, or validation. It therefore serves mainly as a framing of a calibration and consistency question: volatility estimates must be aligned with the option prices and model horizon used in the inversion. It also leaves open how to choose a historical lookback window and whether the model itself should be revised. Any specific recommendation would require additional evidence about the assets, option maturities, data frequency, and pricing framework.

Key ideas

• Stulz's bivariate option formula requires volatility inputs as well as correlation.
• The described workflow infers correlation by inverting option prices after pricing them with a model trained on returns.
• Implied volatility may vary on a different timescale from the model's prices.
• Historical volatility requires a lookback-window choice that the document does not resolve.
• The passage presents an open modeling question and provides no tested alternative volatility estimator.

Tags

# Alternatives to implied or historical volatility for calculating implied correlation


# Alternatives to implied or historical volatility for calculating implied correlation












For my thesis, I'm trying to calculate implied correlation values from bivariate options. I train my model on 10 years of returns data, price the options, and then invert Stulz's Formula (basically Black-Scholes for bivariate options) to find the correlation coefficient given the price. However, Stulz's formula also requires inputs for the asset volatilities. I've tried using the implied volatilities, but they change too quickly relative to the prices from the model to be used. I have the same problem for historical volatility, but also its sort of unclear what time window I should be using. I was trying to think of alternatives for those, but I'm drawing a blank. Are those the only logical things that I could use for asset volatilities? If so, the issue likely lies with my model. Thanks!

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