Serving the Quantitative Finance Community

 
User avatar
Arn
Topic Author
Posts: 0
Joined: January 5th, 2004, 9:33 am

quanto FX options greeks

June 4th, 2010, 10:38 pm

Hi,let's say you have a vanilla FX option EURUSD but quanto'd in say CHF. Physical settlement does not make sense, right?So you can get a CHF PV discounted on CHF and with Black Scholes formula with an appropriate quanto adjustment to the EURUSD forward. Now the greeks. If I call V(XXX) the value of my option expressed in ccy XXX:normally for a normal EURUSD option, delta spot = dV(USD)/dEURUSD, and then delta spot premium is dV(EUR)/dUSDEUR (ie same but seen from the other end).giving delta spot premium = delta spot + V(USD)...Now for a quanto option like above, I don't know if the same numbers have the same meaning or even a meaning at all.The delta spot would be dV(CHF) / dEURUSD (sensitivity to the underlying, ok).But the delta spot premium? Would I need one and what would it be what would it tell me?Or would dV(USD)/dEURUSD and dV(EUR)/dUSDEUR have more significance than dV(CHF)/ dEURUSD?thanks in advance anyone,Arn
 
User avatar
fxotrader
Posts: 0
Joined: November 6th, 2011, 3:02 pm

quanto FX options greeks

January 8th, 2012, 7:21 pm

first of all, you are correct, this will not be physically delivered, it will just cash settle in CHF at a specified rate, which of course as you have pointed out adds CHF risk to this optioni think you're confusing yourself with underlyings. the issue here that you're not addressing properly is that now you have three underlying spots, EURUSD, USDCHF, and EURCHFlet's take for example a EURUSD call option cash settling into CHFclearly you are long EUR and short USD from the vanilla aspect of the option, and long CHF since you want the value of the cash settlement to be greater when you get it.. this translates into deltas of long EURUSD, short USDCHF, short EURCHF.. when viewing your risk you'll of course just look at the net EUR, USD, and CHF deltas so you can hedge them in an efficient manner (the long EURUSD should overpower the short EURCHF to leave you net long EUR)... these deltas will be sensitivity to the other underlyings, i.e. you'll have cross gamma like d(USDCHF delta)/d(EURUSD spot) as well as regular gammahope this helps you out