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!

  • 1
    $\begingroup$ Instead of using a fixed number for implied volatility, you should use a distribution based on your observations for realized and implied volatility. You can then randomly sample from this distribution to get a distribution for the implied correlation. The volatility might not matter that much. Then again, the implied correlation could be very sensitive to volatility, in which case an implied correlation value might not be useful to begin with. $\endgroup$
    – JPN
    Commented Apr 12, 2019 at 22:12
  • $\begingroup$ I will try this. Thanks! $\endgroup$
    – Jason
    Commented Apr 14, 2019 at 18:37


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