So as opposed to the normal structure using a reference temperature and HDD/CDD, I'm looking at pricing a call option with a structure similar to the following:
Daily option on maximum daily temperature over a particular threshold where said temperature maps to an incrementally increasing quantity to use when calculating payout against a price index average during a particular timeframe. There is a "strike price" in that there is no payout unless the average price exceeds a threshold as well. There is a daily and aggregate maximum payout (where this gets complicated for me). So, for example:
Day 1:
Max temp = 101
Corresponding quantity = 200
Avg price = 700 dollars per unit
Payout = 700*200 = 14,000
Day 2:
Max temp = 102
Corresponding quantity = 300
Avg price = 800 dollars per unit
Payout = 800*300 = 21,000
Day 3:
Max temp = 98 (does not exceed temperature strike - would not exercise)
Corresponding quantity = 0
Avg price = 50 dollars per unit
Payout = 0*50 = 0
Day 4:
Max temp = 110
Corresponding quantity = 1000
Avg price = 2000 dollars per unit
Payout = 1000*2000 = 2,000,000 -> payout max of 500,000 = 500,000
Also recall that as we proceed through the contract period, there is some aggregate payout max as well per contract.
Any thoughts on how to think about this from a pricing perspective?