Weather Derivatives Research Articles

Contracting with Controllable Risk

ABSTRACT We examine how executives' ability to control their firms' exposure to risk affects the design of their incentive-compensation contracts. Our natural experimental evidence shows that exchange-traded weather derivatives allow executives to control their firms' exposure to weather risk. Once these derivatives became available, those executives who use them to hedge experience relative reductions in their total compensation and equity incentives. The decline in compensation is consistent with a reduction in the risk premium that executives receive for exposure to weather risk. The decline in equity incentives is consistent with the relation between risk and incentives shifting in a complementary direction when executives can better control their firms' exposure to risk. Collectively, our findings provide evidence that executives' ability to control their firms' exposure and, by extension, their own to an important source of risk influences the design of their incentive-compensation contracts. JEL Classifications: G32; J33; J41.

Pricing Wind Power Futures

AbstractWith increasing wind power (WP) penetration an extensive amount of volatile and weather dependent energy is fed into the German electricity system. To manage the volume risk of windless days and the transfer of revenue risk from wind turbine owners to investors, WP derivatives were introduced. These insurance-like securities allow the hedging of the volume risk of unstable WP production on exchanges such as NASDAQ and EEX. We present a modern and powerful methodology to model weather derivatives, with very skewed underlying assets, incorporating techniques from extreme event modelling to tune seasonal volatility. We compare transformed Gaussian and non-Gaussian CARMA(p, q) models. Our results indicate that the Gaussian CARMA(p, q) model is preferred over the non-Gaussian alternative. Out-of-sample backtesting results show good performance, with respect to benchmarks, employing smooth market price of risk (MPR) estimates based on NASDAQ weekly and monthly German WP futures prices. A seasonal MPR of a smile shape is observed, with slightly positive values in times of high volatility, for example, winter months, and negative values, in times of low volatility and production, for example, in summer months. We conclude that producers pay premiums to insure stable revenue steams, while investors pay premiums when weather risk is high.

Weather Risk Assessment for Collective Water Supply and Sewerage Systems

The weather derivatives market as an instrument of effective weather risk management is still not flexible enough for many industries. The water supply and sewerage industry is sensitive primarily to heavy rainfalls and periods of high and low temperatures: days with heavy rainfall may cause a hydraulic overload of the sewerage systems; on hot days, the water demand increases significantly; on frost days, the risk of water pipe failure grows. The work aimed to summarise methods of weather risk management and propose indices that will help to protect the interests of the water supply and sewerage industry in Poland. Three indices were proposed: a daily precipitation index, frost day index, and hot day index. The frequency of reaching these indices in Poland was verified with the use of meteorological data from 1970–2019, for 19 locations. The non-parametric Mann-Kendall test was used to determine the climate change impact on the exceedance frequency of the proposed indicators. The results showed that the indexes were exceeded in the past once every 6 years, on average. The hot day index was exceeded the least often, but it was the only one with a clear (growing) trend observed.

Risk hedging strategies for electricity retailers using insurance and strangle weather derivatives

With the increase of extreme weather events and the penetration of distributed energy resources, electricity retailers will encounter more risks at both transmission and distribution levels during the business operation process. For risks at the transmission level, huge damages to the transmission lines and towers caused by extreme events, like bushfires, ice storms, and flooding, will lead to power shortage. For risks at the distribution level, demand variations in accordance with temperature change will result in energy procurement difficulty for the retailers. In this paper, besides the normal bilateral contract, the insurance, the strangle weather derivatives, and the energy storage system are implemented to hedge the risks at both the transmission and distribution levels. Simulation results show that the proposed model ensures higher profits for the retailers in summer and winter compared to the conventional model when there are no extreme events occurring. When there are extreme events in both summer and winter, the proposed model incurs lower reduction of profits than that of the conventional model. In brief, the overall profits of the retailer using the proposed hedging model are higher than the convention model, and the overall profit variation of the conventional model is about 26% higher than the proposed model. Furthermore, when the budget of the retailer is sufficient, all three hedging tools can be invested. Whereas when the budget of the retailer is limited, the investment order should be insurance the first, strangle weather derivatives the second, and energy storage system the third.

Gambling on the Monsoon in the Indian Desert

In the desert area of Rajasthan, people have been betting money on when and how much it will rain during the monsoon for centuries. Despite state investment in forecasting technologies in India, rain bettors do not believe official weather data can predict the precise timing, volume, or location of rain. They instead observe the sky and share real-time information via social networks. Ethnographic research on weather prediction has focused on farmers’ expertise and information relevant for agriculture. Rain betting highlights other monsoon patterns in northwest India, especially sudden shifts in cloud direction and speed. It also foregrounds a creativity around weather uncertainties that, like weather derivatives trading, is about pursuit of profit through active ongoing engagement with weather risks. Rain betting, I argue, is a form of vernacular speculation in futures in an area where people are increasingly giving up farming for more profitable work.

Valuation and Risk Management of Weather Derivatives: The Application of CME Rainfall Index Binary Contracts

Valuation and Risk Management of Weather Derivatives: The Application of CME Rainfall Index Binary Contracts

Climate risks and weather derivatives: A copula-based pricing model

The paper focuses on the role of climate and weather derivatives (CDs/WDs for short) as instruments to hedge climate risk. The aim of this paper is twofold: (i) we introduce a copula-based pricing methodology for multivariate CDs/WDs, whose flexible theoretical framework allows to be suited to any pricing application and possible structure of multivariate products, and (ii) we discuss the impact of CDs/WDs on climate risk and their implication for financial stability. Using the proposed framework, we illustrate a calibration example on a case study on Italian data. We find that Archimedean copula functions characterized by left tail dependence are generally more suitable to fit the data, depending on the season and the location. We also explore the advantages of using more sophisticated, i.e. multivariate, functions and assess the improvement of fitting. Subsequently, leveraging both the theoretical model and the empirical results, we discuss the relation between climate risk hedging and financial stability. Especially, we move from modeling complexities and limitations to illustrate how incorrect calculations (i.e. mispricings, or over/under estimations of capital at risk) can, alongside with climate change effect, increase rather than reduce the climate physical risk and hence the concerns for financial stability. Finally, we discuss this point in relation with the legislative framework, noting how, in the current context of uncertain legislation and imperfect pricing, climate hedging risks are likely to do more harm than good.

Simultaneous hedging strategy for price and volume risks in electricity businesses using energy and weather derivatives

In general, electric utilities face intrinsic risks as their revenues depend on high volatility factors including price and volume of sales/procurements. Aiming for an effective strategy to control those risks, we construct a hedging portfolio based on energy and weather derivatives, which can minimize the revenue fluctuations. To this end, we provide unique methods by applying nonparametric regression techniques to synthesize the payoff functions of derivatives that change with time, based on tensor product spline functions. The proposed methodology enables us to incorporate two dimensional smoothing conditions of the underlying asset price and expiration date with a yearly cyclical trend. Moreover, we show that the applied method of Analysis of Variance (ANOVA) decomposition can separate deterministic time trends from the original multivariate payoff functions, and hence, a simultaneous estimation of multiple derivatives payoff functions is achieved. By assuming that revenues have yearly cyclical trends even when viewed at the rate of annual change, we also introduce a spline function with cross variables to consider such a mixed effect. In addition, we propose new standardized derivatives with the square of the temperature prediction error as the underlying asset. Empirical analysis using data from both the Japan Electric Power Exchange (JEPX) and PJM in the U.S. demonstrates the significant hedging effect and supports the versatility of the proposed modeling approach.

New weather indices for China: based on DCC-GARCH and GRU models

Because China is a major production and operations hub, it is at the centre of the world's supply chain. However, as weather can significantly affect supply chain operations, to better hedge risk, weather derivatives need to be introduced to Chinese financial markets to secure multinational supply chains. Using historical records over a decade, three models are proposed and new weather indices are created and improved using DCC-GARCH and GRU models. A simulation test from 2008 to 2017 data proved the indices to be feasible and stable, and matched 92% of the risk across two dimensions: 1) the changing Chinese weather data; 2) a connection with US weather index.

On Modelling and Pricing Weather Derivatives Driven by Nonlinear Brownian Motion

In this paper, our focus is to derive the estimates satisfied by the risk-neutral prices of a class of weather derivatives, contingent upon temperature which satisfies G-stochastic differential equation driven by nonlinear G-Brownian motion.

New weather indices for China: based on DCC-GARCH and GRU models

Because China is a major production and operations hub, it is at the centre of the world's supply chain. However, as weather can significantly affect supply chain operations, to better hedge risk, weather derivatives need to be introduced to Chinese financial markets to secure multinational supply chains. Using historical records over a decade, three models are proposed and new weather indices are created and improved using DCC-GARCH and GRU models. A simulation test from 2008 to 2017 data proved the indices to be feasible and stable, and matched 92% of the risk across two dimensions: 1) the changing Chinese weather data; 2) a connection with US weather index.

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.

Managing Meteorological Risk through Expected Shortfall

This paper focuses on weather derivatives as efficient risk management instruments and proposes a more advanced approach for their pricing. An “hybrid” contract is introduced, combining insurance properties, specifically tailored for the region under study and introducing Value-at-Risk (VaR) and Expected Shortfall (ES) as appropriate measures for the strike price. The numerical results show that VaR and ES are both efficient ways for managing the so-called Tail Risk; further, being ES more conservative than VaR and due to its subadditivity property, it can be seen that seasonal contracts are generally better off than monthly contracts in reducing global risk.

Development of an irradiance-based weather derivative to hedge cloud risk for solar energy systems

For large energy consumers transitioning to high shares of solar energy, irradiance variability causes volatility in power generation and energy expenditures. Volatility in an end user’s cash flow is harmful to their financial health, especially in abnormally cloudy years. This paper explores the utility of an irradiance-based weather derivative in mitigating cloud weather risk and measures the effectiveness of the developed derivative by applying it to a case study of two Chilean copper mines. Weather derivatives are financial instruments tied to an underlying weather variable that act as an insurance for the contract holder, executing indemnity payments based on an index value. This research develops a contract with a combined index based on monthly sums of irradiance and cloudy day sequencing to mitigate a solar mine’s weather risk. The design and evaluation of contracts are based on LEELO, a linear optimization model outputting optimal sizes of solar photovoltaic, battery storage, and power-to-gas systems, as well as the operation of these systems for a given mine’s load, irradiance and technology costs. Results indicate contracts are effective in cloudier climates with increasing utility for mines installing solar energy systems until the year 2030. After 2030 batteries begin to become a more cost-effective risk-hedging mechanism as they become more affordable.

The Valuation of Weather Derivatives Using One Sided Crank–Nicolson Schemes

This paper prices weather derivatives of two typical processes: the Ornstein–Uhlenbeck process and the Ornstein–Uhlenbeck process with jump diffusions. Efficient one sided Crank–Nicolson schemes are developed to solve the convection dominated partial differential and integral-differential equation corresponding to the two processes, respectively. For second order convergence, the one sided Crank–Nicolson schemes may utilize piecewise cubic interpolations to approximate the jump conditions in degree days direction. The unconditional stability is then obtained through the local von Neumann analysis. As extensive numerical experiments shown, the schemes are highly efficient and accurate, and can serve as competitive and practical pricing instruments in weather derivative markets.

Weather Derivatives and the Market Price of Risk

Weather Derivatives and the Market Price of Risk

A temperature stochastic model for option pricing and its impacts on the electricity market

Electricity use varies with the weather as changes in temperature and humidity affect the demand for space heating and cooling. The residential end-use sector has the largest seasonal variance with significant spikes in demand every summer and winter. Electricity demand is subject to fluctuations on a seasonal basis, across the week, and during the day and can also be influenced by irregular events. The demand for power fluctuates significantly in the electricity market resulting in significant ancillary costs to suppliers. This article describes weather derivatives in electricity markets and applies the risk management hedging technique for the price fluctuation and electricity demand during weather variations. The main objective of this paper is to construct a temperature stochastic model for option pricing and determine its impact on electricity markets. We begin by briefly considering the construction of the temperature stochastic model under a Fractional Brownian motion which is driven by the fractional Itô formula and the fractional Girsanov theorem. We then extend this staging to the weather derivative market and construct a stochastic model for bond weather derivatives and financial derivatives (weather options). Following that, we construct and derive the option-pricing model from the Black–Scholes equation and build a pricing model for weather derivative instruments based on the weather contribution of the electricity market. Finally, we carried out a numerical example that allows us to see that the predicted option pricing values might differ depending on how temperature is forecasted.

APPLICATION OF AIR DERIVATIVE FINANCIAL INSTRUMENTS IN LITHUANIAN ECONOMY

The paper explores the concept of weather derivatives: what it is, what its features are, and in what areas they can be applied. It has been established that there can be several types of weather derivative instruments – options and swaps. The use of weather derivatives has also been found to be very broad and attractive for tourism, construction, agriculture and heating companies. Companies operating in Lithuania do not use weather derivatives, although they do provide insurance against the risks associated with adverse weather conditions. The paper is conducting a study to determine which heating companies should apply weather derivatives to improve their performance. The study is conducted using multi-criteria assessment methods – SAW and TOPSIS. The multi-criteria assessment showed that AB Šiaulių energija and UAB Varėnos šiluma could use the opportunity to apply weather derivatives in their activities.

Extracting pricing densities for weather derivatives using the maximum entropy method

In this paper we propose the use of the maximum entropy method to extract pricing densities directly from the weather market prices. The proposed methodology can overcome the data sparsity problem that governs the weather derivatives market and it is model free, non-parametric, robust and computationally fast. We propose a novel method to infer consistent pricing probabilities, and illustrate the method with a motivating example involving market prices of temperature options. The probabilities inferred from a smaller subset of the data are found to consistently reproduce out-of-sample prices, and can be used to value all other possible derivatives in the market sharing the same underlying asset. We examine two sources of the out-of-sample valuation error. First, we use different sets of possible physical state probabilities that correspond to different temperature models. Then, we apply our methodology under three scenarios where the available information in the market is based on historical data, meteorological forecasts or both. Our results indicate that different levels of expertise can affect the accuracy of the valuation. When there is a mix of information available, non-coherent sets of prices are observed in the market.

Pricing of weather derivatives based on temperature by obtaining market risk factor from historical data

A stochastic model driven by generalized hyperbolic Levy process with seasonal mean and volatility for the daily average temperature data is used. This model is perfect to capture the semi-substantial tails and skewness observed in our data. The model is fitted to 11 years of daily data recorded in 16 cities of Ethiopia. We obtained the market risk factor from the historical data of temperature by calculating the CDD and HDD, which is a new addition to the concept of weather derivatives and main contribution of this paper. We get a promising result which enable us to obtain more accurate value for price of temperature derivative. Moreover, the price of weather derivative written on temperature indices is calculated, using Monte Carlo simulation technique. Numerical examples are presented to indicate the accuracy of the method. Our results show that the model performs well to predict CDD and HDD indices.