FX Option Pricing Under a Central Bank Exchange Rate Cap

Summary

The document considers how to value currency options when a central bank caps an exchange rate, using the Swiss National Bank’s franc ceiling against the euro as context. Its answer argues that standard models calibrated to historical market behavior may be unreliable when intervention changes the market regime. In that setting, anticipating the central bank’s responses and their effect on trading may matter more than applying a model built on past price patterns.

The response suggests that intervention could include selling short-dated gamma to encourage market participants to help defend the cap. It presents this as a potentially valuable market insight, not as a calibrated pricing framework or a tested strategy. The discussion is brief and offers no equations, data, or readable references. Its warning is specific to situations where official action dominates price formation; it does not establish that option models are always useless or explain how to quantify intervention risk in an option valuation.

Key ideas

• Central bank intervention can disrupt historical relationships used to calibrate currency option models.
• When an exchange rate is capped, predicting the authority’s response may be more informative than relying on past market behavior.
• The answer suggests that central bank trading in short-dated gamma could help participants enforce a currency ceiling.
• The document offers a qualitative warning, not a formal pricing method or empirical test.

Tags

# How should FX options be priced when a currency is artificially capped?


# How should FX options be priced when a currency is artificially capped?












The question is inspired by yesterday's (06/09/11) historic announcement by the Swiss National Bank that it would impose a ceiling on the franc of 1.20 against the euro.

I would like to know if there are any standard models to value currency options and quantos when the currency exchange rate is effectively capped by the central bank.

Could anyone point to good readable references? A quick web search did not show anything relevant.

## Answer by Tal Fishman (score 3)

https://quant.stackexchange.com/a/1893

I don't believe there are any models because it would be fruitless to develop one. Whenever central bank intervention looms large in currency markets, all the traditional models become much less relevant than trying to predict how the central bank will react to various scenarios. In this case, foreseeing the SNB's move to sell a significant quantity of short-dated gamma in an effort to get markets to help them enforce the ceiling would have been much more lucrative than application of any artificial model. Models must necessarily be estimated from historical data. The moves happening in the EUR/CHF market these days are completely outside the norms established over the last 10+ years of trading.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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