this is my very first question in this forum, after having been a greed follower since a few years, feeling that I need your help in a topic.
I need to price a multi asset option that has the structure of a collar, and get the full value of it plus its greeks. My first thought was to use a Montecarlo with reduced variance, and then apply Kirk's equation However, given the multi asset feature and the fact that Im in front of 3 different assets not properly correlated (TTF gas and two oil products - plus fx component as gas = eur and oil prod = usd) I found a paper of Pellegrino and Sabino on using moment matching, that as far as I know is also used in the pricing of asian options.
Does anyone have an idea on how to implement it, though, and how to deal with the stochastic correlation? My intention was to use the IV by taking ATM vol and just a normal correlation with historical variance/covariance
any input appreciated. also, I thought in implementing it on MATLAB
many thanks everyone