Extracting Information from the Market to Price the Weather Derivatives

Weather derivatives were first launched in 1996 in the United-States to allow companies to protect themselves against weather fluctuations. Even now their valuation still remains tricky. Because their underlying is not a traded asset, the weather options cannot be priced by using the Black and Scholes formula. Other pricing methods were proposed but they cannot be calibrated to the market since there are no available weather option price. However, quoted prices exist for the weather futures. The purpose of this paper is to extract two types of information from these prices, the risk-neutral distribution and the market price of risk, to value the weather derivatives. The prices are calculated by assuming that the daily average temperature obeys a mean-reverting jump-EGARCH process since it is shown that the temperature is not normally distributed and exhibits a time-varying volatility.weather derivatives; incomplete market; mean-reverting jump diffusion process; EGARCH process; PIDE; inversion problem

Which Method for Pricing Weather Derivatives ?

Since the introduction of the first weather derivative in the United-States in 1997, a significant number of work was directed towards the pricing of this product and the modelling of the daily average temperature which characterizes most of the traded weather instruments. The weather derivatives were created to enable companies to hedge against climate risks. They respond more to a need to cover seasonal variations which may cause loss of profits for companies than to a coverage need in property damage. Despite the abundance of work on the topic, no consensus has emerged so far about the methodology for evaluating weather derivatives. The major problems of these instruments are on one hand, they are based on an meteorological index that is not traded on financial market which does not allow the use of traditional pricing methods and on the other hand, it is difficult to get round this obstacle by susbtituting the underlying for a linked exchanged security since the weather index is weakly correlated with prices of other financial assets. To further the question of evaluation, we propose in this paper to, firstly, shed light on the difficulties of implementing the three major pricing approaches suggested in the literature for the weather derivatives (actuarial, arbitrage-free and consumption-based methods) and, secondly, to compute the prices of a weather contract by the three methodologies for comparison.weather derivatives; arbitrage-free pricing method; actuarial pricing approach; consumption-based pricing model; risk-neutral distribution; market price of risk; finite difference method; Monte-Carlo simulations.

Sunshine-Factor Model with Treshold GARCH for Predicting Temperature of Weather Contracts

Climate changes have sparked growing interest for the weather derivatives which are financial contracts relied on a meteorological index and allowing companies to hedge against climate risk. These contracts present the particularity of providing compensation to the buyer when the meteorological index crossed a limit agreed in advance with the seller. In order to evaluate these products and to manage at best the risks associated with their exchange, it is important to be able to accurately predict the evolution of the climate variable. Several processes have been proposed in the literature to model the behaviour of the temperature which is the basis of most of the traded weather instruments. These processes relate mainly to the univariate time series modelling which is founded on the study of the autocorrelation of the stationary variable. But we know that the behaviour of the temperature can be influenced by climatic factors such as rain, wind or sunshine. In our paper, we propose to take into account the impact of sunshine on the temperature as well as the asymmetric effect of the shocks on the volatility by estimating a structural model with a periodic threshold GARCH. We show that this model provides better out-sample forecasts for 30 and 60 days ahead than those obtained by the univariate autoregressive-conditional heteroskedasticity process.weather derivatives; structural model; Markov chain; threshold GARCH; Monte-Carlo simulations; Value-at-Risk.

Utility-based Pricing of the Weather Derivatives

Since the underlying of the weather derivatives is not a traded asset, these contracts cannot be evaluated by the traditional financial theory. Cao and Wei (2004) price them by using the consumption-based asset pricing model of Lucas (1978) and by assuming different values for the constant relative risk aversion coefficient. Instead of taking this coefficient as given, we suggest in this paper to estimate it by using the consumption data and the quotations of one of the most transacted weather contracts which is the New York weather futures on the Chicago Mercantile Exchange (CME). We apply the well-known generalized method of moments (GMM) introduced by Hansen (1982) to estimate it as well as the simulated method of moments (SMM) attributed to Lee and Ingram (1991) and Duffie and Singleton (1993). This last method is studied since it is presumed to give satisfactory results in the case of the weather derivatives for which the prices are simulated. We find that the estimated coefficient from the SMM approach must have improbably high values in order to have the calculated weather futures prices matching the observations.weather derivatives; consumption-based asset pricing model; constant relative risk aversion utility function; generalized method of moments; simulated method of moments; HAC matrix; Monte-Carlo simulations; periodic variance; GARCH

Pricing the Weather Derivatives in the Presence of Long Memory in Temperatures

Weather derivatives are financial contracts for which the underlying is not a traded asset. Therefore, they cannot be priced by the traditional financial theory based on the hedging portfolio and on the arbitrage-free argument. Some authors suggest to use the actuarial pricing approach to value the weather derivatives. But this method suffers from the fact that it is only based on the modelling of the temperature. The market information is not necessary to value the weather derivatives by this approach. On the contrary, the financial method needs to infer the market price of weather risk since the market is incomplete for the weather derivatives. We suggest in this paper to compute and to compare the prices stemming from the both approaches by using the New York weather futures quotations. Prices are calculated on the basis that the daily average temperature has a long memory since tests reveal its presence in the serie.weather derivatives; incomplete market; long memory; ARFIMA process; FIGARCH process; LMSV process; fractional Brownian motion; PDE; Monte-Carlo simulations

Which Method for Pricing Weather Derivatives ?

Since the introduction of the first weather derivative in the United-States in 1997, a significant number of work was directed towards the pricing of this product and the modelling of the daily average temperature which characterizes most of the traded weather instruments. The weather derivatives were created to enable companies to hedge against climate risks. They respond more to a need to cover seasonal variations which may cause loss of profits for companies than to a coverage need in property damage. Despite the abundance of work on the topic, no consensus has emerged so far about the methodology for evaluating weather derivatives. The major problems of these instruments are on one hand, they are based on an meteorological index that is not traded on financial market which does not allow the use of traditional pricing methods and on the other hand, it is difficult to get round this obstacle by susbtituting the underlying for a linked exchanged security since the weather index is weakly correlated with prices of other financial assets. To further the question of evaluation, we propose in this paper to, firstly, shed light on the difficulties of implementing the three major pricing approaches suggested in the literature for the weather derivatives (actuarial, arbitrage-free and consumption-based methods) and, secondly, to compute the prices of a weather contract by the three methodologies for comparison

Sunshine-Factor Model with Treshold GARCH for Predicting Temperature of Weather Contracts

Climate changes have sparked growing interest for the weather derivatives which are financial contracts relied on a meteorological index and allowing companies to hedge against climate risk. These contracts present the particularity of providing compensation to the buyer when the meteorological index crossed a limit agreed in advance with the seller. In order to evaluate these products and to manage at best the risks associated with their exchange, it is important to be able to accurately predict the evolution of the climate variable. Several processes have been proposed in the literature to model the behaviour of the temperature which is the basis of most of the traded weather instruments. These processes relate mainly to the univariate time series modelling which is founded on the study of the autocorrelation of the stationary variable. But we know that the behaviour of the temperature can be influenced by climatic factors such as rain, wind or sunshine. In our paper, we propose to take into account the impact of sunshine on the temperature as well as the asymmetric effect of the shocks on the volatility by estimating a structural model with a periodic threshold GARCH. We show that this model provides better out-sample forecasts for 30 and 60 days ahead than those obtained by the univariate autoregressive-conditional heteroskedasticity process

Utility-based Pricing of the Weather Derivatives

Since the underlying of the weather derivatives is not a traded asset, these contracts cannot be evaluated by the traditional financial theory. Cao and Wei (2004) price them by using the consumption-based asset pricing model of Lucas (1978) and by assuming different values for the constant relative risk aversion coefficient. Instead of taking this coefficient as given, we suggest in this paper to estimate it by using the consumption data and the quotations of one of the most transacted weather contracts which is the New York weather futures on the Chicago Mercantile Exchange (CME). We apply the well-known generalized method of moments (GMM) introduced by Hansen (1982) to estimate it as well as the simulated method of moments (SMM) attributed to Lee and Ingram (1991) and Duffie and Singleton (1993). This last method is studied since it is presumed to give satisfactory results in the case of the weather derivatives for which the prices are simulated. We find that the estimated coefficient from the SMM approach must have improbably high values in order to have the calculated weather futures prices matching the observations

ECONOMETRIE DES SERIES TEMPORELLES

LicenceTutorial in French on the basic principles of the time series modellingTutoriel en francais sur les principes de base de la modelisation des series temporelle

Evaluation des dérivés climatiques sur degrés-jours

The introduction of the first weather derivative based upon the degree-days in the United-States in 1997 has led to a great number of work dedicated to the valuation of this product and to the modelling of the daily average temperature. However until now, no empirical study has compared all together the pricing approches and the temperature models which were suggested in the literature. Therefore in the present thesis, we set out to compute the prices of the weather futures and call options from the free-arbitrage, actuarial and consumption-based methods.We were particularly interested in the pricing of the contracts on the degree-days of Chicago, Cincinnati and New York for which frequent transactions were observed. The linked analysis of the estimated prices of the weather futures from the different pricing methodologies has shown that the calibration of the pricing models was necessary to obtain predictions of the prices which were closed to the quotations and more particularly to the real realization of the index on degree-days at the expiration date.L'introduction sur le marché financier du premier dérivé climatique portant sur les degrés-jours en 1997 aux Etats-Unis, a donné lieu à un nombre important de travaux sur la valorisation des instruments climatiques et sur la modélisation de la température moyenne journalière. Cependant, aucune étude conjointe de l'ensemble des approches d'évaluation et des représentations de la température suggérées dans la littérature n'avait été menée jusqu'à présent sur le plan empirique. Nous nous sommes donc proposés dans la présente thèse de calculer les prix des contrats à terme et des options d'achat climatiques à partir des méthodes en l'absence d'arbitrage, actuarielle et fondée sur la consommation. Nous nous sommes particulièrement intéressés au calcul des prix des contrats sur les degrés-jours des villes de Chicago, de Cincinnati et de New York pour lesquelles nous avions constaté des transactions fréquentes sur le Chicago Mercantile Exchange. L'analyse conjointe des cours estimés des contrats à terme climatiques à partir des différentes méthodologies d'évaluation a montré que le calibrage des modèles d'évaluation était nécessaire pour obtenir des prévisions de prix proches des cotations et plus particulièrement de la réalisation réelle de l'indice des degrés-jours à l'échéance