I'm trying to price a CSO on Soyoil. The instrument is extremally illiquid. To proceed, I simulate both leg by Monte Carlo, using the historical correlation over the 75past days and their respective ATM Implied Volatility. For each simulations of both leg in a row, I impose the correlation with a Cholesky decomposition and I subtract Jan to Dec to get the spread. The distribution of the spreads values look quite normal on the last day of simulation (at expiration). Then by taking the average of max(0,S-K) and discounting by exp(-rt) I get the price of the option which is systematically much lower than the bid-ask on the market.
Taking the implied vol ATM is an assumption, I believe it models the spread with the actual market view of volatility of both legs.
Are there better ways to price extremally illiquid CSO ? I'm trying to understand how to model at best the spreads distribution at expiration. If someone has any knowledge about this topic, please feel free to share it here.
Many thanks !