Modeling VWAP Premiums as a Function of Intraday Volatility

Summary

The document defines a VWAP premium as the daily volume-weighted average price divided by the closing price, minus one. The author observes heteroskedasticity in this measure and a scatterplot association in which larger absolute premiums tend to occur on days with higher intraday volatility. This motivates modeling the size of the premium using intraday volatility as an explanatory variable.

The question is how to fit such a relationship when changing variance appears linked to an external predictor rather than past volatility, as in a standard GARCH setup. The proposed product of intraday volatility and another volatility term is posed as a possibility, not established as a fitted model. No estimation method, data results, or Python implementation is provided, so the observed association should be treated as exploratory rather than evidence of a validated predictive relationship.

Key ideas

• The VWAP premium is defined relative to the closing price.
• The observed scatterplot associates higher intraday volatility with larger absolute VWAP premiums.
• The question frames heteroskedasticity as potentially conditional on an external explanatory variable.
• A multiplicative volatility specification is suggested but not fitted or validated in the document.
• The plotted association is exploratory and does not establish predictive performance.

Tags

# Fitting model between security price and intraday volatility


# Fitting model between security price and intraday volatility












I'm trying to construct a model which shows how much the closing price of a security ($P_t$) differs from the VWAP of that security on that day ($VWAP_t$). I'm calling this measure the "VWAP Premium": $$VWAP_{premium} = \frac{VWAP_t}{P_t}-1$$ By simply plotting this for the MSCI ACWI ETF, I see that it exhibits heteroskedasticity, but not necessarily any other trend:

One thought I had was that intraday volatility ($\sigma_{ID}$) could help signal these larger absolute values of $VWAP_{premium}$, so I plotted the scatterplot and it does indeed look like that's the case:

Days with larger intraday volatilities also are more likely to have larger absolute VWAP Premiums, which is intuitive enough. My question is, how is this model fitted? It's not a GARCH model, since the heteroskedasticity is not dependent on prior volatility, but on another variable altogether. It seems to me like this would be something like:

$$VWAP_{premium} = (\sigma_{ID})(\sigma_{VWAP})$$

Is there a simple way to fit this model in Python?

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