CB currency pegging & FX reserves

[JTDerp]

Any good references on the math behind currency pegging by central banks as a function of:

- the bank's balance sheet

- market prices of the 'master' currency...specifically, how the bank traders (try to) ensure the currency to be pegged stays within the float range spec'd? Do they just watch intraday market action and come in with counter-acting orders where needed? Or some more structural way?



This harkens back to Soros & BoE, but I'm taking interest moreso from recent comments by Kyle Bass about Hong Kong's balance sheets vs USD.

[Strange]

maybe this:

https://files.stlouisfed.org/files/htdocs/publications/review/01/09/0109md.pdf



In a less rigorous way, something or other can be based on the square root volume/impact model:



dP = alpha * volatility * sqrt(quantity/volume)



i.e. if you have a band that's dP percent away for a currency with a given volatility and volume, you'd need to spend



volume * (dP /(alpha * volatility))^2



to prevent that boundary from being breached. Of course, value of alpha is calibrated from the experience of the CB traders and there is also a question of estimating volume and volatility in a crisis.

[nikol]

Pegging is not only about trading but can involve a range of intervention tools.



https://www.bis.org/publ/bppdf/bispap24d.pdf



https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2474011

[rickyvic]

I have never done any calculations but my educated guess is that this limits might work for a small country and so illiquid currencies which you can trade through NDF against certain banks.

As already mentioned for large countries this is not going to matter compared to policy making.



It is an interesting topic though and that soros vs boe story always fascinated me.