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?