# How to think about pricing this weather call option

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.

The common approach to temperature derivatives in their first run of popularity (in the late 1990's) was to use an Ornstein-Uhlenbeck process to describe deviations of temperature from a seasonal average. So far as I know, no major innovations have arisen since then.

Calibrating such a model is very simple, and so is valuing certain quantities such as degree day calls. Your payoff is complex enough that you will need to price it using Monte Carlo simulation instead.

• Had gotten as far as Ornstein-Uhlenbeck to model temps. Good to know that it's still latest and greatest among practitioners. Thanks. Mar 16, 2012 at 15:17

WARNING * I'd seriously think carefully while pricing this especially using temperature as the underlying, becasue you need to nail a value to temperature.

How much does 1 degree cost? Weather markets are seriously incomplete. What location / index would you use as the reference for temperature?

By the way have a read of H Gemans paper on pricing weather derrivates:

http://www.emeraldinsight.com/journals.htm?articleid=1463233&show=abstract

Hope this little post of mine helps.

• Thanks for the reference. I will take a read of it shortly. Mar 16, 2012 at 19:49