pricing quanto options: which vol for forward drift?

mspadaccino · October 29th, 2009, 3:25 pm

Hihas anyone thought about which equity volatility should be used in the quanto adjustment (i.e. vol_equity x vol_fx x corr_Eq_fx) in the standard BS environment when the option is not at the money?Shall I use two different parameters (i.e. volatility taken on the strike of listed, vanilla products for the normal BS part of the formula, and volatility taken on the ATM Spot level for the part involving the quanto adjustment) or should it be used a single parameter (vol. on the strike) for both sections?What is your thought about it?thanks

mixmasterdeik · December 21st, 2009, 6:01 pm

If you are in a standard BS world there is no smile. So all vols are the sameWhen you have a smile this is mapped into LV for diffusions causing the following drift:drift = sigma_eq(S,t) * sigma_fx(FX,t) *rho(t), where sigma(S,t) is the LV for the equity diffusion and sigma(FX,t) is the local vol for the FX diffusionCheers

Speedy · December 22nd, 2009, 4:59 am

For an interesting discussion on quanto adjustments, you can have a look at Peter Jaeckel's recent articel "Quanto Skew": http://www.awdz65.dsl.pipex.com/QuantoSkew.pdf