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:
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A is the average of daily mean temperatures in Chicago over July 1–31, and
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K is the strike.
Assume you have a historical time series of daily mean temperatures for Chicago (multiple years).
(a) Modeling the index A
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Propose a practical statistical model for the distribution of A that accounts for: (i) seasonality, (ii) daily autocorrelation, and (iii) non-Gaussian tails/extremes.
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Specify how to estimate all model parameters from historical data.
(b) Pricing approaches
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Present both actuarial and risk-neutral pricing methods. State clearly the assumptions each requires.
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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
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Outline a Monte Carlo algorithm to estimate the option price and a 95% confidence interval.
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Derive how to choose the number of simulation paths to achieve ±$0.05 precision on the price estimate.
(d) Cooling Degree Days (CDD)
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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?