August 17th, 2005, 5:20 am
In currency markets we have option on the base pair and the option on the derived pair. For e.g. option on USDFCY and option on EURUSD.. now if i want to have option on EURFCY .. i find correlation between USDFCY and EURUSD.. i have the vol of USDFCY and EURUSD.. i find vol for EURFCY and price the option accordingly.. Since i have used the two underlying vols for pricing.. i would like to use the same for hedging the option as well.. hence is it right to use underlying options to hedge the cross option.. And if so then how do i offset the various greeks between the three options..Some simulations i have run on this led to following observation..1. Using this methodology gives rise to residual delta which has to be hedged so that any change in correlation does not affect the position much.2. For small changes in spot the P&L is almost squareLiterature suggests that the ratio of the two option need not be exactly 1. Here I need help. If somebody has come across some closed form solution which suggests the ratio of the option such that we have minimum vairance portfolio.Further, I wanted to know for estimating correlation what is a good observation periodAnd for rolling correlation is there a preference on which window should be considered..i.e. 90 days or 180 daysThanks and RegardsJP