Weather Derivatives Research Articles

Approaching rainfall-based weather derivatives pricing and operational challenges

This article approaches some of the current rainfall derivatives pricing and operational challenges through an empirical application to Comunidad Valenciana, Spain. Regarding the former, two different issues are addressed. First, we examine the rightness of suggesting the Gamma distribution to price rainfall contracts, which is the alternative chosen by previous authors applying the Index Value Simulation technique. This is done for the purpose of determining whether the consideration and comparison of other alternatives may lead to more accurate valuation results. Concretely, two different distributions, in addition to the Gamma, are proposed: the exponential and the mixed exponential, whose fits are assessed through the Kolmogorov–Smirnov/Lilliefors test and graphical analyses. The outcomes attained indicate that this selection process leads indeed to a precise generation of the rainfall index’s moments. Next, we examine the viability of using a unique distribution to model the rainfall risk of regions located nearby, since this would considerably decrease valuation complexity. Our analysis shows that the most convenient choice depends on the period and location considered, although the mixed exponential appears as a reasonable option in most cases. Finally, a relevant operational challenge related to geographical basis risk is approached. Concretely, an evaluation of this type of risk among the locations studied is conducted. The results attained indicate that, given the insufficient degree of correlation between nearby locations, rainfall risk hedging measures may rely on compound derivatives referred to several neighbor stations.

Forecasting Daily Residential Natural Gas Consumption: A Dynamic Temperature Modelling Approach

In this paper, we propose a methodology to forecast residential and commercial natural gas consumption which combines natural gas demand estimation with a stochastic temperature model. We model demand and temperature processes separately and derive the distribution of natural gas consumption conditional on temperature. Natural gas consumption and local temperature processes are estimated using daily data on natural gas consumption and temperature for Istanbul, Turkey. First, using the derived conditional distribution of the natural gas consumption we obtain confidence intervals of point forecasts. Second, we forecast natural gas consumption by using temperature and consumption paths generated by Monte Carlo simulations. We evaluate the forecast performance of different model specifications by comparing the realized consumption values with the model forecasts by backtesting method. We utilize our analytical solution to establish a relationship between the traded temperature-based weather derivatives, i.e. HDD/CDD futures, and expected natural gas consumption. This relationship allows for partial hedging of the demand risk faced by the natural gas suppliers via traded weather derivatives.

Hedging Weather and Catastrophe Risks using Commodity Futures as Weather Derivatives in India

Hedging Weather and Catastrophe Risks using Commodity Futures as Weather Derivatives in India

Pricing Basket Weather Derivatives on Rainfall and Temperature Processes

This paper follows an incomplete market pricing approach to analyze the evaluation of weather derivatives and the viability of a weather derivatives market in terms of hedging. A utility indifference method is developed for the specification of indifference prices for the seller and buyer of a basket of weather derivatives written on rainfall and temperature. The agent’s risk preference is described by an exponential utility function and the prices are derived by dynamic programming principles and corresponding Hamilton Jacobi-Bellman equations from the stochastic optimal control problems. It is found the indifference measure is equal to the physical measure as there is no correlation between the capital market and weather. The fair price of the derivative should be greater than the seller’s indifference price and less than the buyer’s indifference price for market viability and no arbitrage opportunities.

A regime switching model for temperature modeling and applications to weather derivatives pricing

In this study, we propose a regime-switching model for temperature dynamics, where the parameters depend on a Markov chain. We improve upon the traditional models by modeling jumps in temperature dynamics via the chain itself. Moreover, we compare the performance of the proposed model with the existing models. The results indicate that the proposed model outperforms in the short time forecast horizon while the forecast performance of the proposed model is in line with the existing models for the long time horizon. It is shown that the proposed model is a relatively better representation of temperature dynamics compared to the existing models. Furthermore, we derive prices of weather derivatives written on several temperature indices.

Is temperature-index derivative suitable for China?

In this paper, we assessed the suitability of temperature derivatives for China through modeling. We assumed that if the physical dynamics of temperature of some cities are identical, then the same types of temperature derivatives can be used in these cities. Nearly twenty years temperature data of forty-seven cities with traded temperature derivatives on the Chicago Mercantile Exchange Group (CME) and seven Chinese cities were collected and analyzed in a two-step approach. Firstly, the AR-EGARCH model capturing the shock asymmetry of the volatility of temperature is used to simulate the dynamics of temperature of the cities. Secondly, the temperature of the cities are classified through cluster analysis based on model parameters from the AR-EGARCH model. The results showed that the fitting effect of the AR-EGARCH model is very good, and only a few cities did not display the shock asymmetry. The model for Nanjing fitted well into one of the categories of the cities in the CME; but the other six Chinese cities belong to new categories, which are different from the cities in the CME. We concluded that HDD and CAT in Europe and CAT∗ in Japan can be used directly in Nanjing, but the existing temperature derivatives in CME were unsuitable for the other six Chinese cities. Recommendations for the establishment of weather derivatives market in China have been proposed.

Modeling and pricing of space weather derivatives

This article proposes a pricing model for space weather derivatives with payout depending on solar activity. By measuring the disturbance of the Earth’s magnetosphere, it is possible to price space weather derivatives which trigger a payoff if a certain level of energization is reached. Since energetic particles emitted by the Sun are a non-tradeable quantity, unique prices of contracts in an incomplete market are obtained using inverse transformation sampling as well as the market price of risk. We find a step-wise decline of option prices with increasing barriers of Kp-index values, a dependence of the option prices on the sunspot cycle, as well as reduced sensitivity of longer-dated maturities for higher Kp-index values.

Weather impact on retail sales: How can weather derivatives help with adverse weather deviations?

Weather affects four basic purchasing decisions: what, where, when and in what quantity to buy. Retailers are familiar with general impact of weather on consumption and consequential seasonality in retail sales, but lack detail knowledge about precise relationship between weather and sales needed for operational, strategic and financial decision making. Using the non-alcoholic beverages as an example, we conduct thorough weather sensitivity analysis in large food stores and propose design of customized weather derivatives as tools for offsetting failed sales due to adverse weather. We use method of panel which can be generalized to other product categories and other weather sensitive industries. Results show that weather sensitivity of beverages sales varies between months, implying the need for different weather risk management strategies, and that non-alcoholic beverages are bought impulsively rather than planned.

Rainfall Derivatives and Risk Management in the Wine Sector

Since their first introduction in 1996, weather derivatives have been a topic of discussion. The ongoing climate change has, in fact, increased the risks for companies that are naturally exposed to meteorological variables, raising questions on how such companies should manage these increasingly significant risks. The wine sector is one of the most exposed to these risks, including rainfall risk. The purpose of this work is to evaluate the use of rainfall derivatives to create a strategy for managing rainfall risk. For this purpose, both put and call options are implemented. The pricing is carried out by Monte Carlo simulations, based on a model capable of simulating daily rain. Then, rainfall derivatives are applied to the Italian wine regions of the province of Trento and of Franciacorta, and an assessment of the profitability of companies purchasing such derivatives is made to understand their effectiveness in reducing rainfall risk.

Stochastic model genetic programming: Deriving pricing equations for rainfall weather derivatives

Abstract Rainfall derivatives are in their infancy since starting trading on the Chicago Mercantile Exchange (CME) in 2011. Being a relatively new class of financial instruments there is no generally recognised pricing framework used within the literature. In this paper, we propose a novel Genetic Programming (GP) algorithm for pricing contracts. Our novel algorithm, which is called Stochastic Model GP (SMGP), is able to generate and evolve stochastic equations of rainfall, which allows us to probabilistically transform rainfall predictions from the risky world to the risk-neutral world. In order to achieve this, SMGP's representation allows its individuals to comprise of two weighted parts, namely a seasonal component and an autoregressive component. To create the stochastic nature of an equation for each SMGP individual, we estimate the weights by using a probabilistic approach. We evaluate the models produced by SMGP in terms of rainfall predictive accuracy and in terms of pricing performance on 42 cities from Europe and the USA. We compare SMGP to 8 methods: its predecessor DGP, 5 well-known machine learning methods (M5 Rules, M5 Model trees, k-Nearest Neighbors, Support Vector Regression, Radial Basis Function), and two statistical methods, namely AutoRegressive Integrated Moving Average (ARIMA) and Monte Carlo Rainfall Prediction (MCRP). Results show that the proposed algorithm is able to statistically outperform all other algorithms.

Determining the Asset Value of Weather Derivatives for K-League Soccer Clubs

Determining the Asset Value of Weather Derivatives for K-League Soccer Clubs

Hedging Risk with Derivatives in the Rain-Sensitive Hospitality Industry

Weather is a fundamental resource for tourism, but adverse meteorological events (such as persistent rain) need to be considered by hospitality firms because of the increasing economic damages they cause. The study adds to the weather derivative and tourism literature by advancing a model for the rainfall risk management of hospitality firms. It aims to show, in two steps, how hospitality firms could share the risks caused by rain with counterparties by adopting a rainfall derivative to mitigate the negative impacts of rain on profitability. In particular, the first step of the proposed model is based on scenario correlation between business performances and rain. The second step introduces rainfall derivatives and analyzes their impact on the earnings before interest and taxes of hospitality firms. The model is supported by a numerical application covering the decade 2005 to 2014 and based on the business performances of 25 hotels located on Lake Garda, Italy and on the amount of rainfall on that lake.

Mitigating geographical basis risk of weather derivatives using spatial-temporal regime-switching temperature model

In this paper, geographical basis risk in weather derivative design and pricing is mitigated by using spatial-temporal pricing models. A two-state regime-switching temperature model is constructed and extended to multi-dimensional locations that are highly correlated in temperature. The normal and shifted regime of this model are characterized by a heteroscedastic Ornstein-Uhlenbeck process and a Brownian motion with mean different from zero respectively. The correlation between the driving noise in each regime is assumed to be a function of the space between the locations and increases with decreasing space. A weight is assigned to each location in the temperature basket. However, a location with a higher risk is assigned a larger weight and vice versa. The weightings in the temperature basket gave considerable importance to farming locations having greater exposure to temperature risk. The further the farming location from the weather station, the larger the weight. With this spatial-temporal weather derivatives pricing model, the holder of a weather derivative contract will have the opportunity to select the most appropriate composite of weather stations with their desired weight that can reduce geographical basis risks.

A new approach to evaluating the cost-efficiency of complex hedging strategies: an application to electricity price–volume quanto contracts

Electricity quanto contracts improve the efficiency of financial risk management by accommodating the correlated price and volumetric risks of energy suppliers. The use of electricity quanto contracts, however, suffers from the high risk premiums associated with such tailor-made and illiquid financial instruments. As a result, it is of great interest to properly evaluate the cost-efficiency of these complex hedging deals. To address this concern, we propose a new hedging assessment model, the economic value of the incremental expected shortfall (EVIES), from a cost-efficiency perspective. Using EVIES, we develop a Monte Carlo simulation-based hedging framework. This framework overcomes the limits of traditional models by not resting on risk neutrality, market completeness or unobservable inputs. In our numerical examples, we assume that a fictitious power supplier has access to electricity price derivatives, weather derivatives and electricity quanto contracts, and we show that our proposed model can be applied to: (1) construct a cost-effective hedge against an electricity price–volume joint risk, (2) find a partial equilibrium for the valuation of electricity quanto contracts and (3) locate hedging solutions for achieving a specific risk management target.

Intelligent Methods Used for Obtaining Weather Derivatives: A Review

Weather is the condition of the atmosphere and forecasting is predicting the condition of the atmosphere in near future. Weather forecasting is a formidable challenge as weather is a multi- dimensional, continuous and chaotic process. The distinct nature of the model forecasting in all situations accurately is challenging. Presently weather conditions are being obtained from satellites, Doppler radar, radio sounds, observations from aircraft and ground. Collected data is subjected to various statistical and machine learning techniques. These techniques can incorporate relatively simple observation of the sky to highly complex computerized mathematical models. Weather forecasting still remains a challenging issue, due to unpredictable and chaotic nature of weather. Even with present methods the weather forecasting system may still fail to predict weather attribute, therefore there is still scope left to improve these systems. The objective of carrying out the survey is to look forward on how machine learning can help us to improve weather parameter estimation. In this paper we report the different methods carried out by leading researchers, formidable challenges and present our views on development of efficient weather forecasting system. Also, we propose a method which makes use image processing and neural networks to achieve the weather parameter estimation.

Cross Hedging Using Prediction Error Weather Derivatives for Loss of Solar Output Prediction Errors in Electricity Market

Predicting future solar conditions is important for electricity industries with solar power generators to quote a day-ahead sales contract in the electricity market. If a prediction error exists, the market-monitoring agent has to prepare another power generation resource to immediately compensate for the shortage, resulting in an additional cost. In this context, a penalty may be required depending on the size of the prediction error, which may lead to a significant loss for solar power producers. Because the main source of such losses is from prediction errors of solar conditions, they can instead effectively utilize a derivative contract based on solar prediction errors. The objective of this work is to provide such a derivative contract, namely, a prediction error weather derivative. First, defining a certain loss function, we measure the hedge effect of the derivative on solar radiation prediction error, thereby verifying that the existing hedging method for wind power can also be applied to solar power generation with periodic trends. By introducing the temperature derivative on the absolute prediction error, we also propose a cross-hedging method, where we demonstrate not only a further variance reduction effect when used with solar radiation derivatives, but also a certain hedge effect obtained even when only the temperature derivative is used. For temperature derivative pricing and optimal contract volume estimation, we propose a method using a tensor-product spline function that simultaneously incorporates the smoothing conditions of both the direction of intraday time trend and seasonal trend, and consequently verify its effectiveness.

Comparing the Hedging Effectiveness of Weather Derivatives Based on Remotely Sensed Vegetation Health Indices and Meteorological Indices

Abstract Weather derivatives are considered a promising agricultural risk management tool. Station-based meteorological indices typically provide the data underlying these instruments. However, the main shortcoming of these weather derivatives is an imperfect correlation between the weather index and the yield of the insured crop, called basis risk. This paper considers three available remotely sensed vegetation health (VH) indices, namely, the vegetation condition index (VCI), the temperature condition index (TCI), and the vegetation health index (VHI), as indices for weather derivatives in a German case study. We investigated the correlation and period of highest correlation with winter wheat yield. Moreover, we analyzed whether the use of remotely sensed VH indices for weather derivatives can reduce basis risk and thus improve the performance of weather derivatives. The two commonly used meteorological indices, precipitation and temperature sums, were employed as benchmarks. Quantile regression and index value simulation were used for the design and pricing of the weather derivatives. The analysis for the selected farms and corresponding counties in northeastern Germany revealed that, on average, the VHI resulted in the highest correlation with winter wheat yield, and VHI-based weather derivatives were also superior in terms of the hedging effectiveness. The total periods of the highest correlations ranged from the beginning of April to the end of July. VHI- and VCI-based weather derivatives led to statistically significant reductions of basis risk, compared to the benchmarks. Our results indicate that the VHI-based weather derivatives can be useful alternatives to meteorological indices, especially in regions with sparser weather station networks.

Exploring the financial risk of a temperature index: a fractional integrated approach

This paper introduces a new temperature index, which can suitably represent the underlying of a weather derivative. Such an index is defined as the weighted mean of daily average temperatures measured in different locations. It may be used to hedge volumetric risk, that is the effect of unexpected fluctuations in the demand/supply for some specific commodities—of agricultural or energy type, for example—due to unfavorable temperature conditions. We aim at exploring the long term memory property of the volatility of such an index, in order to assess whether there exist some long-run paths and regularities in its riskiness. The theoretical part of the paper proceeds in a stepwise form: first, the daily average temperatures are modeled through autoregressive dynamics with seasonality in mean and volatility; second, the assessment of the distributional hypotheses on the parameters of the model is carried out for analyzing the long term memory property of the volatility of the index. The theoretical results suggest that the single terms of the index drive the long memory of the overall aggregation; moreover, interestingly, the proper selection of the parameters of the model might lead both to cases of persistence and antipersistence. The applied part of the paper provides some insights on the behaviour of the volatility of the proposed index, which is built starting from single daily average temperature time series.

Financial Sector Stress and Risk Sharing: Evidence from the Weather Derivatives Market

I examine the effect of financial sector stress on risk sharing in a novel setting: the CME’s weather derivatives market. The structure of the market allows me to disentangle price movements due to financial sector stress from price movements due to fundamentals. Contracts, which are typically priced near their actuarially fair value, experience significant price declines during periods of financial sector stress. Contracts with greater margin requirements and total risk are the most affected. The results provide causal evidence of the effect of financial sector stress on the pricing of exchange-traded financial contracts and risk sharing in the economy. Received July 21, 2017; editorial decision July 22, 2018 by Editor Philip Strahan. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

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.