Have you considered using a local volatility model that includes mixtures of log normals

<t>I'm interested in the number of stocks involved in the contract because if there isn't too many ( say less than 10 ) then I can see a way of making the pay off continuous without causing any computational problems. A continous pay off may be of interest to someone trying to hedge the Himalayan ? ...

Does anyone know how many stocks are typically involved in a Himalayan Option ?