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Int J Environ Res Public Health. 2019 Dec 4;16(24). pii: E4882. doi: 10.3390/ijerph16244882.

An Actuarial Pricing Method for Air Quality Index Options.

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School of Economics and Management, Shaanxi University of Science and Technology, Xi'an 710021, China.
China Institute for Urban Governance, Shanghai Jiao Tong University, Shanghai 200030, China.
Sino-US Global Logistics Institute, Shanghai Jiao Tong University, Shanghai 200030, China.
School of Arts and Sciences, Shanxi University of Science & Technology, Xi'an 710021, China.
Appraisal Center for Environment and Engineering, Ministry of Environmental Protection, Beijing 100012, China.
School of Automotive Studies, Tongji University, Shanghai 201804, China.
Shanghai Environment Monitoring Center, Shanghai 200235, China.


Poor air quality has a negative impact on social life and economic production activities. Using financial derivatives to hedge risks is one of the important methods. Air quality index (AQI) options are designed to help enterprises cope with the operational risk caused by air pollution. First, the expanded Ornstein-Uhlenbeck model is established using an autoregressive-generalized autoregressive conditional heteroscedasticity (AR-GARCH) method to predict AQI for a city. Next, the average AQI is constructed to be as the underlying index for the AQI options. We then priced AQI options using an actuarial method with an Esscher transform. Meanwhile payoff functions for the options are established to let enterprises hedge against the operational risk caused by air pollution. Finally, we determined the price of AQI options using data from Xi'an, China, and the example of a tourism enterprise as a case study of how AQI options can be applied to hedge against operational risk for enterprises. With AQI options trading, enterprises can hedge against operational risks caused by air pollution. The applicability of AQI options is wide, it can also be applied in other cities or regions.


Ornstein–Uhlenbeck model; actuarial pricing; air quality index; options; risk hedging

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