This article by Glattfelder, Dupuis and Olsen, brought to my attention by a reader, proposes an empirical set of scaling laws that apply to FX markets.
After considering them, in view of devising an interesting indicator for trading, the problem appears to be that these laws mostly concerns averages taken over 5 years, that is a serious limitation for their applicability on a short period of time.
Nonetheless, I identified one, the law (12) that may be of interest, provided some more work:
This law(applied to the total move, *=tm) gives the length of the coastline for a given pair for a year of activity (250 days) as a percentage, relatively to a resolution defined as the directional-change threshold (cf chapter 2.3 in the article).
Considering the case without the transaction costs (an assumption, I think, justified by the small scale considered), I then look at Table A19 to know the parameters of the Law relative to the currency pair I am interested in. For the following I will consider EUR/USD, which is the pair I trade most often, the law therefore becomes :
As I am interested in moves around 10 PIPs, I shall then consider a resolution of 0.001 for EUR/USD, so:
Which gives me a resolution between 12 and 14 PIPs (for the current value of the EUR/USD) since 0.001 is a percentage.
As a result, I get:
This is the annualised length of the coastline, I am more interested in this length for 15 minutes, I therefore have to divide it by 250*24*4, for a result of:
Which is equal to about 520 PIPs (taking 1.35 for EUR/USD) as the length of the coastline for 15 minutes.
This information is the best I can get so far from the scaling laws described in the article. It may be used to determine the width of a channel (volatility), though, even for this, it needs to be included in further calculations (that will likely used the Graph Dimension, or the Hurst exponent). I am currently thinking of ways to do that, and will publish any success I may have with this line of thought in the future.