Skip to content
All library documents

Why Quanto Option Value Can Depend on the FX Rate

Article Quant Q&A · Author: glork
Read the original

Summary

The document asks whether a quanto put can have a nonzero foreign-exchange delta, despite the common impression that quanto options are insensitive to FX. The question describes a case where the put’s calculated FX delta is positive and attributes this intuition to a negative correlation between the underlying asset and the exchange rate, alongside the quanto adjustment.

The answer explains that quanto pricing includes an adjustment involving the volatility behavior of both the underlying and the FX rate. If those volatilities depend on spot levels, as in local-volatility models, the option’s value can depend on both the underlying spot and the FX spot. This clarifies why FX sensitivity can arise in that setting. The response does not derive a delta formula, specify the model assumptions behind the question’s graph, or establish the sign or size of the sensitivity in general. Its conclusion is conditional on spot-dependent volatility functions, so it should not be read as a universal claim about every quanto option model.

Key ideas

  • Quanto pricing includes an adjustment involving underlying and FX volatility.
  • Spot-dependent volatility functions can make option value depend on both spot levels.
  • Local-volatility models are cited as an example of spot-dependent volatility.
  • A nonzero FX delta can therefore occur in the described setting.
  • The answer does not establish a universal delta sign or quantify sensitivity across models.

Tags

OptionsForexDerivatives pricing
Full text
# Delta FX of a quanto put


# Delta FX of a quanto put












I've heard that quanto options are not sensitive to the FX...but when i draw the graph of the FX delta of the put i find a positive value for all K. For very deep ITM quanto put the FX delta is about 14. My 2 cents about this comes from the quanto adjustment. If X increases then S decreases (my correl is neg). Thus my quanto put is more valuable. So the delta FX is pos. So are quanto puts really sensitive to FX ? Tx

## Answer by Gordon (score 3, accepted)

https://quant.stackexchange.com/a/34070

For a quanto option, there is a quanto adjustment which involves the volatility functions of the option underlying asset and the FX rate. Since the volatility functions may depend on the spot levels, in particular, for local volatility functions, then, the quanto option value depends on the spot levels of both the underlying and the FX rate.

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.