RESEARCH ON WEATHER DERIVATIVES PRICING–THE CASE OF SHANGHAI MUNICIPALITY

Originally published in 2005, Weather Derivative Valuation covers all the meteorological, statistical, financial and mathematical issues that arise in the pricing and risk management of weather derivatives. There are chapters on meteorological data and data cleaning, the modelling and pricing of single weather derivatives, the modelling and valuation of portfolios, the use of weather and seasonal forecasts in the pricing of weather derivatives, arbitrage pricing for weather derivatives, risk management, and the modelling of temperature, wind and precipitation. Specific issues covered in detail include the analysis of uncertainty in weather derivative pricing, time-series modelling of daily temperatures, the creation and use of probabilistic meteorological forecasts and the derivation of the weather derivative version of the Black-Scholes equation of mathematical finance. Written by consultants who work within the weather derivative industry, this book is packed with practical information and theoretical insight into the world of weather derivative pricing.

The weather largely affects economic activity, and thus, companies vulnerable to weather risk need to plan ahead to cope with unexpected weather changes, just as they do for changes in interest rates, oil prices, or foreign exchange rates to stabilize their earning stream. Weather derivatives can be a useful tool for weather risk management. This paper focuses on pricing one of the most popular weather derivatives -HDD/CDD options- and estimating the market price of weather risk (MPR). Historical data are used to construct the stochastic process of temperature, while the current market prices of Chicago and New York HDD futures options are used to extract the implied MPR. The Monte-Carlo Simulation Method is proposed to estimate the price of weather derivatives numerically. In addition, the approximate closed form formula for the options is provided modifying the Alaton, Djehiche, and Stillberg (2002) model. Finally, option price sensitivity to changes in MPR is analyzed to show the important role of the MPR in the weather option pricing model.

Weather derivatives play a major role in risk management of non-catastrophic weather market. The healthy development of the derivatives market is inseparable from the reasonable pricing of the product itself. As non-traditional financial derivatives, weather derivatives can provide a good risk hedging. Meanwhile, in the weather derivatives market, brokers play an even more important part than in the traditional financial derivatives market. Therefore, when pricing weather derivatives, we must take two factors into consideration, namely, brokers as market makers as well as the impact of their hedging cost on weather derivatives pricing. Based on the expected claims and risk payment of basic derivatives contracts, this paper is going to discuss weather derivatives pricing on the basis of hedging costs, while taking into account the impact of market makers’ hedging costs, risk aversion and existing positions.

Weather derivatives play a major role in risk management of non-catastrophic weather market. The healthy development of the derivatives market is inseparable from the reasonable pricing of the product itself. As non-traditional financial derivatives, weather derivatives can provide a good risk hedging. Meanwhile, in the weather derivatives market, brokers play an even more important part than in the traditional financial derivatives market. Therefore, when pricing weather derivatives, we must take two factors into consideration, namely, brokers as market makers as well as the impact of their hedging cost on weather derivatives pricing. Based on the expected claims and risk payment of basic derivatives contracts, this paper is going to discuss weather derivatives pricing on the basis of hedging costs, while taking into account the impact of market makers’ hedging costs, risk aversion and existing positions.

Weather derivatives designed to manage casual changes of weather, as opposed to catastrophic risks of weather, are relatively a new class of financial instruments. There are still many theoretical and practical challenges to the effective use of these instruments. The objective of this paper is to develop a pricing approach for valuing weather derivatives and presents a case study that is practical enough to be used by the risk managers of electrical utility firms. Utilizing daily average temperature data of Guangzhou, China from <TEX>$1^{st}$</TEX> January 1978 to <TEX>$31^{st}$</TEX> December 2010, this paper adopted a univariate time series model to describe weather behavior dynamics and calculates equilibrium prices for weather futures and options for an electrical utility firm in the region. The results imply that the risk premium is an important part of derivatives prices and the market price of risk affects option values much more than forward prices. It also demonstrates that weather innovation as well as weather risk management significantly affect the utility's financial outcomes.

In this text, Fractional Brown Motion theory during random process is applied to research the option pricing problem. Firstly, Fractional Brown Motion theory and actuarial pricing method of option are utilized to derive Black-Scholes formula under Fractional Brown Motion and form corresponding mathematical model to describe option pricing. Secondly, based on BYD stock, estimation model on volatility of this stock is given to analyze and calculate the stock price volatility. Finally, make instance analysis for BYD’s option. Based on market data of BYD’s stock and option, calculate the actual option price and theoretical price of BYD by BlackScholes formula under Fractional Brown Motion. Compare the forecast price of this stock option given by model with actual price, relatively good effect is obtained, and then conclude that the model has relatively strong applicability.

In this text, Fractional Brown Motion theory during random process is applied to research the option pricing problem. Firstly, Fractional Brown Motion theory and actuarial pricing method of option are utilized to derive Black-Scholes formula under Fractional Brown Motion and form corresponding mathematical model to describe option pricing. Secondly, based on BYD stock, estimation model on volatility of this stock is given to analyze and calculate the stock price volatility. Finally, make instance analysis for BYD's option. Based on market data of BYD's stock and option, calculate the actual option price and theoretical price of BYD by Black-Scholes formula under Fractional Brown Motion. Compare the forecast price of this stock option given by model with actual price, relatively good effect is obtained, and then conclude that the model has relatively strong applicability.

PurposeThe paper aims to examine theoretically valuation of weather derivatives and their hedging roles in corporate risk management.Design/methodology/approachThe paper introduces an extended financial market model in which the weather risk is included as an independent random process and examines the effectiveness of weather derivatives and traditional price forwards in a unified theoretical framework. It also provides a no‐arbitrage approach to price weather derivatives, which theoretically combines the actuarial and financial paradigms.FindingsThe results document that corporate leverage level is an essential factor determining the choice between price forwards and weather derivatives. In some cases; weather derivatives outperform price forwards, while in some other cases; a joint use of both instruments is optimal, depending on the firm's risky leverage level. Interestingly, the paper identifies the case when the leverage level is very high, the positive roles of both instruments diminish and the firm is unhedgeable.Originality/valueThe paper provides important insights to investors and hedgers and extends the literature on corporate risk management.

PurposeSmall farmers in developing countries have very little means of managing the weather‐risk to their agricultural produce. Weather derivatives could provide a solution, but the demand for such instruments and the willingness to invest in them needs to be researched. The purpose of this paper is to assess weather‐risk hedging by farmers, focusing on the willingness to pay in Rajasthan, India.Design/methodology/approachThe paper presents results of a contingent valuation study done on the findings of a survey carried out in six villages in the state of Rajasthan. The survey was done on over 500 farmers after explaining the concept of weather derivatives and how they would work to help them hedge their weather‐related yield risk. The survey included questions on factors, which could have a bearing on the farmers' willingness to pay, and a bidding game where responses were solicited to premiums in a hypothetical market. Probit and logit models are used to determine probabilities of “Yes” responses to various bids and the mean willingness‐to‐pay.FindingsThe paper brings out a model, which uses nine independent variables affecting the probability of a farmer saying “Yes” to a price quoted to him for a weather derivative. Using the results from the probit and logit models, the farmers' mean willingness‐to‐pay is determined to be around 8.8 per cent of the maximum possible payout of a weather derivative contract.Originality/valueWith weather derivatives being accepted as a means of risk management for agriculture in developing countries, the willingness‐to‐pay figures determined in this paper would provide an insight to the structuring and pricing of weather derivatives, especially in developing countries.

The standard indices used in the US weather derivatives market are based on monthly and seasonal heating degree days in winter and monthly and seasonal cooling degree days in summer. The pricing of weather options necessitates estimating the distribution of possible values for these indices. We assess to what extent it is safe to assume that these distributions can be modelled using a normal distribution.

Weather derivatives are financial contracts that allow entities to hedge themselves against the adverse impacts of fluctuations in the weather. The pricing of such contracts is based on a combination of actuarial and arbitrage methods. Risk management of portfolios of weather derivatives centres on the estimation of two distributions: the expiry distribution and the short term risk distribution. These distributions can be used to calculate the expiry VaR and the VaR, respectively. The expiry distribution can be estimated relatively easily using the actuarial methods used to price contracts and manage portfolios. The short term risk distribution, however, is much more difficult to estimate since it depends on market dynamics and the statistics of changes in probabilistic meteorological forecasts. Nevertheless, we show that, under certain reasonable assumptions, the short term risk distribution for a large class of standard contracts takes a particularly simple form. It depends on a single volatility that can be derived without having to perform any statistical analysis of past forecasts. In addition we show that the framework we develop for calculating the short term risk distribution leads to a simple method for the actuarial valuation of options during the contract period.

In this study we discuss the pricing of weather derivatives whose underlying weather variable is temperature. The dynamics of temperature in this study follows a two state regime switching model with a heteroskedastic mean reverting process as the base regime and a shifted regime defined by Brownian motion with nonzero drift. We develop mathematical formulas for pricing futures and option contracts on heating degree days (HDDs), cooling degree days (CDDs) and cumulative average temperature (CAT) indices. The local volatility nature of the model in the base regime captures very well the dynamics of the underlying process, thus leading to a better pricing processes for temperature derivatives contracts written on various index variables. We use the Monte Carlo simulation method for pricing weather derivatives call option contracts.

This paper examines the economics and pricing of weather derivatives in Ontario and argues that weather derivatives and weather insurance can be used as a form of agricultural insurance. Using historical data, the relationship between crop productivity and weather is examined. Then a variety of put and call options for rain- and heat-based weather risk are discussed and numerically evaluated. The evaluation examines in detail the pricing of insurance contracts at a given location and across space.

Forecasting based pricing of Weather Derivatives (WDs) is a new approach in valuation of contingent claims on nontradable underlyings. Standard techniques are based on historical weather data. Forward-looking information such as meteorological forecasts or the implied market price of risk (MPR) are often not incorporated. We adopt a risk neutral approach (for each location) that allows the incorporation of meteorological forecasts in the framework of WD pricing. We study weather Risk Premiums (RPs) implied from either the information MPR gain or the meteorological forecasts. The size of RPs is interesting for investors and issuers of weather contracts to take advantages of geographic diversification, hedging eects and price determinations. By conducting an empirical analysis to London and Rome WD data traded at the Chicago Mercantile Exchange (CME), we find out that either incorporating the MPR or the forecast outperforms the standard pricing techniques.

This paper examines the quantification of uncertainty in weather derivatives pricing. The focus is on the propagation of a posterior distribution on uncertain model parameters through to relevant payoff statistics, summarizing the uncertainty using variance based credible intervals for any given payoff statistic. We also demonstrate the use of sensitivity analysis to determine the most influential parameters on the credible interval size. This paper serves a multitude of purposes. Firstly, we provide a basic review of the underlying theory behind uncertainty/sensitivity analysis, along with authors' novel ideas for numerical implementation. We also provide a novel and informative set of numerical results for credible interval computation and sensitivity analysis for a market relevant 5-station temperature problem. This paper serves as a foundation for exploring the use of Bayesian uncertainty/sensitivity quantification in weather derivatives portfolio management.