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I'm trying to understand and interpret this economic formula within research where Implied Volatility is regressed on Realised volatility. But even though I understand the basics of what this article's author is trying to convey, I'm still stumped by this rather complex formula.

Could you please attempt to break down the formula for me? This way I could understand what the elements in the formula refer to and how it's contribute to the formula, just like an Excel sheet would.

The formula looks like this and you can find any other handy information here by going down to "3.3.3 Empirical Models", where we focus on model 1.

Economic Formula

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  • 2
    You might be better off on Quantitative Finance for questions like this, although check their help first.
    – AakashM
    Dec 22, 2023 at 14:03
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    It would be off topic on Quant se because it's just an OLS regression.
    – AKdemy
    Dec 22, 2023 at 16:20
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    @AKdemy was right, it got closed due to being off topic Jan 6 at 6:24
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    Regarding the use of logs, it's a very common transformation. The paper anyhow explains why it's done in this case. Some theory with plenty of graphs can be found in this quant SE answer.
    – AKdemy
    Jan 6 at 16:16

1 Answer 1

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That is a model to apply the least square method to find parameters alpha0 and beta1 to predict the variance of the next time period lnRV(t) from the variance measured in the current time period lnIV(t-1). epsilon(t) is the error term (difference between the actual value and the predicted value). The goal is to get the squared epsilons as small as possible. That's where the name comes from.

So if you want to apply that, you will probably have data for variances of a security paper etc. for time periods 1...t-1 and you want to predict t as well as possible. According to the model, you would do that by taking the data for the first t-2 periods you have as measurements, because you know what the variance for those periods and the following period was. You then can say, that what your prediction for period i (i between 1 and t-2) is, should be as close as possible to what you actually measured for period i+1.

To get this you look at the sum for i from 1 to t-2 over epsilon(i)^2 and chose the parameters alpha0 and beta1 so they get minimal. You just need to consider, that the error is calculated as epsilon(i)=InRV(i)-InIV(i).

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  • I don't understand, why they do not render TeX formulas here. It would be much easier to read!
    – jottbe
    Dec 22, 2023 at 13:18
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    Mathjax isn't supported on money se because it's usually just simple stuff (that's the assumption).
    – AKdemy
    Dec 22, 2023 at 14:02
  • @jottbe It would be annoying to have to escape dollar signs. But it seems like there should be a way of addressing tham. Jan 6 at 6:09

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