Monday, June 13, 2011

rho of a vanilla fx option

(See post on theoretical greeks)

For equity options, it's known that rho is a relatively insignificant sensitivity compared to the big 4 greeks. I know FX rates are sensitive to the 2 interest rates involved. What's the rho of a FX option?
A: insignificant.


where :

From FX-modified BS formula, we can tell rho is equally insignificant for equities vs forex.  However, a 10bps bump in either rd or rf will immediately(?) affect S, more in forex than in equities. I believe an rate hike makes a currency attractive at least in the short term
Answer: (from a young FX quant) even though spot forex rate S0 is influenced (less than fwd forex rate) by  rd or rf, we still assume S0 is an independent variable when we bump rd or rf. There's no mathematical justification to adjust S0 when we bump the rates. Therefore for short dated FX options, rho is insignificant.

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