Price a temperature-based weather option
Overview
This question evaluates competencies in statistical time-series modeling (seasonality and autocorrelation), heavy-tailed/extreme-value modeling, parameter estimation, pricing of weather derivatives, and Monte Carlo-based uncertainty quantification, and is commonly asked to assess the ability to integrate data-driven modeling with market pricing and risk-loading considerations. It falls under the Statistics & Math domain with overlap into quantitative finance and data science, and tests both conceptual understanding of modeling and pricing frameworks and practical application skills for calibration, simulation, and precision control.
Weather Derivative on July Temperatures: Modeling, Pricing, and Simulation
You are valuing a European call option on weather. The payoff at the end of July is (A − K)+, where:
- A is the average of daily mean temperatures in Chicago over July 1–31, and
- K is the strike.
Assume you have a historical time series of daily mean temperatures for Chicago (multiple years).
(a) Modeling the index A
- Propose a practical statistical model for the distribution of A that accounts for: (i) seasonality, (ii) daily autocorrelation, and (iii) non-Gaussian tails/extremes.
- Specify how to estimate all model parameters from historical data.
(b) Pricing approaches
- Present both actuarial and risk-neutral pricing methods. State clearly the assumptions each requires.
- Explain how to calibrate a market price of weather risk (or equivalent risk loading) from available market quotes on similar weather contracts.
(c) Monte Carlo pricing and precision
- Outline a Monte Carlo algorithm to estimate the option price and a 95% confidence interval.
- Derive how to choose the number of simulation paths to achieve ±$0.05 precision on the price estimate.
(d) Cooling Degree Days (CDD)
- How would your modeling and pricing change if the payoff were instead based on Cooling Degree Days (e.g., July CDD), rather than the average temperature A?
Solution
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