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The cost of market impact is usually modeled as:

$$ \Delta{P} = \delta \sigma (\frac{Q}{V})^{1/2} $$

Where:

  • $ \Delta{P} $ is the change in price of the asset caused by the transaction size $Q$
  • $\sigma$ is a measure of price volatility (units of price)
  • $ V $ is a measure of trading volume
  • $ Q $ and $ V $ have the same units (both are dollars, or number of shares)
  • $ \delta $ is a dimensionless coefficient of order 1

How one produces estimates of these parameters affects how quickly market impact costs fluctuate.

If, for instance, price volatility $\sigma$ is estimated from just the last $n$ 10-minute-frequency open, high, low, and close ("ohlc") prices (using Yang-Zhang volatility or similar), estimated volatility will vary rapidly if $n$ is small, or will vary slowly if $n$ is large. The same applies to estimating the volume $V$.

The goal should be to model the real market impact of a trade well. In my case, I want to accurately model it in small markets (daily dollar volume ~$100K).

So how rapidly should I expect market impact costs (estimated from $\sigma$ and $V$) to fluctuate? In other words, what should $n$ be, or how should it be chosen?

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