Cumulative Average Temperature Research Articles

Weather derivatives for managing weather and climate risk in agriculture

In this paper, we develop a pricing model for weather derivatives at a single location and multiple locations. In the first model, a Lévy regime-switching temperature model for a single location is used to price futures written on cumulative average temperature and growing degree-days indices at a single location. To allow analytical pricing for futures on temperature basket, an [Formula: see text]-dimension regime-switching temperature model whose driving noise is captured by a Brownian motion is developed. The correlation between the driving noise in each regime is assumed to be a function of the space between the different farming locations and increases with decreasing space. The temperature basket index assigns a weight to each location that is exposed to risk. However, a location with a higher risk is assigned a larger weight and vice versa. By assuming that the regimes are independent to each other, the future is calculated for each regime model. The final futures price is calculated using the weighted sum of the individual regimes. These pricing models can be applied in the future markets to price weather derivatives for the agricultural sector. Research on spatial-temporal pricing model is vital to the development of the weather derivatives market, as investors are more vulnerable to temperature risk over different farming locations as compared to single location.

Hedging Crop Yields Against Weather Uncertainties—A Weather Derivative Perspective

The effects of weather on agriculture in recent years have become a major global concern. Hence, an effective weather risk management tool (i.e., weather derivatives) that can hedge crop yields against weather uncertainties is needed. However, most smallholder farmers and agricultural stakeholders are unwilling to pay for the price of weather derivatives (WD) because of the presence of basis risks (product-design and geographical) in the pricing models. To eliminate product-design basis risks, a machine learning ensemble technique was used to determine the relationship between maize yield and weather variables. The results revealed that the most significant weather variable that affected the yield of maize was average temperature. A mean-reverting model with a time-varying speed of mean reversion, seasonal mean, and local volatility that depended on the local average temperature was then proposed. The model was extended to a multi-dimensional model for different but correlated locations. Based on these average temperature models, pricing models for futures, options on futures, and basket futures for cumulative average temperature and growing degree-days are presented. Pricing futures on baskets reduces geographical basis risk, as buyers have the opportunity to select the most appropriate weather stations with their desired weight preference. With these pricing models, farmers and agricultural stakeholders can hedge their crops against the perils of extreme weather.

PRICING TEMPERATURE DERIVATIVES UNDER WEATHER FORECASTS

We investigate the pricing of temperature derivatives under weather forecasts modeled by initially enlarged filtrations. For this purpose, we introduce a mean-reverting temperature model with seasonality and derive expressions for the so-called forward temperature. Although our analysis focuses on cumulative average temperature (CAT) futures, the presented derivation techniques can likewise be applied to other weather derivatives such as heating degree day (HDD) or cooling degree day (CDD) futures, for instance. We also treat option pricing and utility maximizing portfolio selection in temperature markets under additional information on future weather behavior. We finally prove an anticipative sufficient stochastic minimum principle in an enlarged filtration setup and apply the result to minimal variance hedging of temperature derivatives under weather forecasts. In this context, we derive explicit minimal variance hedging portfolios for different weather-related claims.

Weather derivatives pricing using regime switching model

Abstract 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.

Spatial Risk Premium on Weather Derivatives and Hedging Weather Exposure in Electricity

Due to dependency of energy demand on temperature, weather derivatives enable the effective hedging of temperature related fluctuations. However, temperature varies in space and time and therefore the contingent weather derivatives also vary. The spatial derivative price distribution involves a risk premium. We examine functional principal components of temperature variation for this spatial risk premium. We employ a pricing model for temperature derivatives based on dynamics modelled via a vectorial Ornstein-Uhlenbeck process with seasonal variation. We use an analytical expression for the risk premia depending on variation curves of temperature in the measurement period. The dependence is exploited by a functional principal component analysis of the curves. We compute risk premia on cumulative average temperature futures for locations traded on CME and fit to it a geographically weighted regression on functional principal component scores. It allows us to predict risk premia for nontraded locations and to adopt, on this basis, a hedging strategy, which we illustrate in the example of Leipzig.

Pricing and Hedging Temperature Futures Derivatives under Weather Forecasts

We derive risk-neutral option price formulas for plain-vanilla temperature futures derivatives on the basis of several multi-factor Ornstein-Uhlenbeck temperature models which allow for seasonality in the mean level and volatility. Our main innovation consists in an incorporation of omnipresent weather forecasts via numerous tailor-made enlargements of the underlying historical information filtration. In this insider trading framework, we obtain forward-looking price representations for cumulative average temperature (CAT) and cooling degree day (CDD) futures whereas we provide anticipative CAT option price formulas. On this occasion, the evaluation of conditional expectations under enlarged filtrations comprises the major mathematical challenge which we handle by applying suitable transformation concepts from complex analysis. Ultimately, we construct optimal positions in a temperature futures portfolio under future weather information to hedge against both temporal and spatial temperature risk simultaneously.

Spatial Risk Premium on Weather Derivatives and Hedging Weather Exposure in Electricity

Due to the dependency of the energy demand on temperature, weather derivatives enable the effective hedging of temperature related fluctuations. However, temperature varies in space and time and therefore the contingent weather derivatives also vary. The spatial derivative price distribution involves a risk premium. We employ a pricing model for temperature derivatives based on dynamics modeled via a vectorial Ornstein-Uhlenbeck process with seasonal variation. We use an analytical expression for the risk premia depending on variation curves of temperature in the measurement period. The dependence is exploited by a functional principal component analysis of the curves. We compute risk premia on cumulative average temperature futures for locations traded on CME and fit to it a geographically weighted regression on functional principal component scores. It allows us to predict risk premia for nontraded locations and to adopt, on this basis, a hedging strategy, which we illustrate in the example of Leipzig.

Modeling and forecasting cumulative average temperature and heating degree day indices for weather derivative pricing

In this paper, we use wavelet neural networks in order to model a mean-reverting Ornstein–Uhlenbeck temperature process, with seasonality in the level and volatility and time-varying speed of mean reversion. We forecast up to 2 months ahead out of sample daily temperatures, and we simulate the corresponding Cumulative Average Temperature and Heating Degree Day indices. The proposed model is validated in 8 European and 5 USA cities all traded in the Chicago Mercantile Exchange. Our results suggest that the proposed method outperforms alternative pricing methods, proposed in prior studies, in most cases. We find that wavelet networks can model the temperature process very well and consequently they constitute an accurate and efficient tool for weather derivatives pricing. Finally, we provide the pricing equations for temperature futures on Cooling and Heating Degree Day indices.

Putting a Price on Temperature*

Abstract. This paper analyzes the weather derivatives traded at the Chicago Mercantile Exchange (CME), with futures and options written on different temperature indices. We propose to model the temperature dynamics as a continuous‐time autoregressive process with lag p and seasonal variation. The choice p=3 turns out to be sufficient to explain the temperature dynamics observed in Stockholm, Sweden, where we fit the model to more than 40 years of daily observations. The main finding is a clear seasonal variation in the regression residuals, where temperature shows high variability in winter, low in autumn and spring, and increasing variability towards the early summer. Our model allows for derivations of explicit prices for several futures and options. Note that the volatility term structure of futures written on the cumulative average temperature has a modified Samuelson effect, where the volatility prior to the measurement period increases, except for the last part, where it may decrease.