An option can be exercised hourly but depends on two prices - one is available daily and hourly, the other one only daily. How can I write an option model that uses a quadrinomial lattice with both these prices and can be exercised hourly?
Please take the following as given, as I already have a model that serves very well its purpose for daily granularity: I assumed that log-prices (after removing seasonalities) are mean reverting (http://en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_process) and I estimated 2 correlated Ornstein-Uhlenbeck processes from historic spot prices - electricity and gas. Then I wrote an option model that calculates the value of the spread between the two (i.e. a gas power plant) with the possibility to exercise daily (binomial method is convenient, as there are many physical restrictions of the power plant). I want to do the same for HOURLY exercise, but for gas there are only DAILY liquid spot prices.
Is there a way that I can for example infer a hypothetical hourly drift, mean-reversion speed, volatility and correlation with electricity price for gas price from the daily parameters?