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Purpose--The purpose of this paper is to propose a feasible model for the daily average temperatures of Beijing, Shanghai and Shenzhen, in order to price temperature-based weather derivatives; also to derive analytical approximation formulas for the sensitivities of these contracts.
Design/methodology/approach--This study proposes a seasonal volatility model that estimates daily average temperatures of Beijing, Shanghai and Shenzhen using the mean-reverting Omstein-Uhlenbeck process. It then uses the analytical approximation and Monte Carlo methods to price heating degree days and cooling degree days options for these dries. In addition, it derives and calculates the option sensitivities on the basis of an analytical approximation formula.
Findings--There exists a strong seasonality in the volatility of daily average temperatures of Beijing, Shanghai and Shenzhen. To model the seasonality Fourier approximation is applied to the squared volatility of daily temperatures. The analytical approximation formulas and Monte Carlo simulation produce very similar prices for heating/cooling degree days options in Beijing and Shanghai, a result that also verifies the convergence of the Monte Carlo and approximation estimators. However, the two methods do not produce converging option prices in the case of HDD options for Shenzhen.
Originality/value--The article provides important insight to investors and hedgers by proposing a feasible model for pricing temperature-based weather contracts in China and derives analytical approximations for the sensitivities of heating/cooling degree days options.
Keywords China, Temperature distribution, Forecasting, Weather derivatives, Heating degree days options, Cooling degree days options, Monte Carlo simulation
Paper type Research paper
The demand for weather derivatives was initially driven by the energy industry in the USA, where the first over-the-counter weather derivatives were introduced in 1997. Recently, other industries such as utilities, agriculture and tourism are also increasing the demand for weather-contingent financial products. Weather derivatives and their applications in the energy and agriculture industries are discussed in studies by Cao et al. (2007), Ellithorpe and Putnam (1993), Sharma and Vashishtha (2007), Turvey (2001) and Zeng (2000). These industries hedge their investments against weather-related risk, thus stimulating the development of the weather derivatives market. In addition, hedge funds have begun to invest in weather derivative contracts in order to diversify their portfolios, thereby also contributing to the recent growth in these contracts. Finally, the lack of weather derivatives in stock portfolios increases the demand for weather derivative contracts for diversification purposes.
Unlike equity options, the underlying variable in a weather derivative is non-tradable, thus making the weather derivatives market incomplete and perfect hedging impossible. This study mainly prices derivatives by using a dynamic model for temperatures that incorporates the market price of risk based on the market prices of weather derivatives. The model is fired to the temperatures of three Chinese cities, namely Beijing, Shanghai and Shenzhen, and used with Monte Carlo simulation and analytical approximation methods to price weather derivatives.
The next section defines daily temperatures, heating degree days (HDD) and cooling degree days (CDD). Section 3 fits the daily average temperatures of Beijing, Shanghai and Shenzhen between the years of 1990 to 2009 to the dynamic pricing model proposed by Benth and Saltyte-Benth (2007), and uses the fitted model to price HDD and CDD contracts. Section 4 presents the statistical results of Monte Carlo simulation for the HDD and CDD options for Beijing, Shanghai and Shenzhen. It also computes the sensitivities of the prices of those options, and compares the results of analytical approximation with those of Monte Carlo simulation in order to determine the degree of convergence between the two. Lastly, Section 5 provides the conclusion of the study.
2. Temperature-based contracts
Weather derivative contracts include swaps, futures, and call and put options based on different underlying weather indices. Some commonly used indices are HI)D, CDD, rain (precipitation), wind and snowfall. Temperature-based HDD and CDD indices are the most popular indices in the weather derivatives market. The following are the study's definitions of daily temperature and the HDD and CDD indices.