Pricing Capped Weather Options with Temperature and Price Triggers
Summary
The document considers a weather-linked call whose daily payout depends on maximum temperature mapping to a quantity and a price index average exceeding a strike. The payoff also has daily and contract-wide payout limits, making a direct closed-form valuation difficult. The response recommends modeling temperature deviations from a seasonal average with an Ornstein–Uhlenbeck process, a framework historically used for temperature derivatives. While that model can support simpler degree-day valuations, the layered payoff described here calls for Monte Carlo simulation.
The discussion also stresses that temperature-based markets are incomplete: pricing requires defining a reference location or index and deciding how temperature maps to economic value. It offers no calibration data, worked simulation, or numerical fair value, and points to earlier weather-derivatives literature rather than developing the approach. Results would depend on the chosen temperature process, the quantity mapping, price behavior, payout caps, and the contract’s reference specification.
Key ideas
- An Ornstein–Uhlenbeck process can model temperature deviations from a seasonal average.
- Simple degree-day claims may be valued analytically, but layered payoffs may require simulation.
- Monte Carlo can incorporate daily temperature quantities, price triggers, and payout caps.
- A usable valuation requires a defined temperature reference and an economic mapping from degrees to payout.
Tags
Full text
# How to think about pricing this weather call option # 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. Any thoughts on how to think about this from a pricing perspective? ## Answer by Brian B (score 7, accepted) https://quant.stackexchange.com/a/3077 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. ## Answer by Piroinno (score 0) https://quant.stackexchange.com/a/3081 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.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.