Modeling temperature behaviors: Application to weather derivative valuation

• Published date: 01 September 2018
• Author: Chuang‐Chang Chang,Jr‐Wei Huang,Sharon S. Yang
• Date: 01 September 2018
• DOI: http://doi.org/10.1002/fut.21923

1152 © 2018 Wiley Periodicals, Inc. wileyonlinelibrary.com/journal/fut J Futures Markets. 2018;38:1152–1175.

Received: 24 September 2016

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Accepted: 17 March 2018

DOI: 10.1002/fut.21923

RESEARCH ARTICLE

Modeling temperature behaviors: Application to weather

derivative valuation

Jr-Wei Huang

1,2

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Sharon S. Yang

3,4

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Chuang-Chang Chang

3

1

Department of Insurance, Hubei

University of Economics, Wuchang,

Wuhan, Hubei Province, China

2

Institute for Development of Cross-strait

Small and Medium Enterprises, Hubei

University of Economics, Wuchang,

Wuhan, Hubei Province, China

3

Department of Finance, National Central

University, Jhongli City, Taoyuan County,

Taiwan, Republic of China

4

Risk and Insurance Research Center,

College of Commerce, National Chengchi

University, Wenshan District, Taipei City,

Taiwan, Republic of China

Correspondence

Sharon S. Yang, Department of Finance,

National Central University, No. 300,

Jhongda Rd., Jhongli City, Taoyuan County

32001,Taiwan, Republic of China.

Email: syang@ncu.edu.tw

This article investigates temperature behavior to develop a temperature model. The

proposed ARFIMA Seasonal GARCH model that allows for long memory effects and

other important temperature properties provides better goodness of fits and

forecasting accuracy using daily average temperatures in six U.S. cities. The effect

of temperature behavior on pricing temperature derivatives is analyzed. We propose

an equilibrium option pricing framework for HDD and CDD forward and option

contracts under the ARFIMA Seasonal GARCH model. The investigation of

temperature properties and the valuation framework in this study contributes to the

development of a standardized temperature model for weather derivative markets.

KEYWORDS

equilibrium pricing, long memory, temperature derivatives

JEL CLASSIFICATION

C4, C5

1

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INTRODUCTION

Weather has an important influence on various industries, including power, entertainment, agriculture, retail, transportation, and

construction. Worldwide climate changes and abnormal weather have led to significant losses (Impact Forecasting, 2013; IPCC,

2008; Lobell et al., 2007). Recent statistics show that in 2013 the United States suffered economic losses of $17.22 billion due to

severe weather; flooding in central Europe during summer months caused economic losses of $22 billion. Then, drought inChina

between January and August caused losses estimated at $10 billion.

1

Thus, there is a strong need to manage weather risk globally.

The introduction of weather derivatives in the capital market in turn has attracted great attention as a potential tool for

hedging weather risks. Weather derivatives are financial contracts that allow entities to hedge against fluctuations in the weather.

The first weather derivative, issued in 1997, traded on the temperature in the Over the Counter (OTC) market; today the largest

weather derivative market is the Chicago Mercantile Exchange (CME). The latter comprises four location-based subgroups: the

United States and Canada, Europe, Japan, and Australia.

2

Approximately 82% of the contracts refer to the United States and

Canada market; Europe and Asia represent 11 and 7%, respectively (Brockett et al., 2005). In the former, weather derivatives are

1

These statistics come from the Impact Forecasting November 2013 Global Catastrophe Recap.

2

The locations of focal locations are Atlanta, Chicago, Cincinnati, New York, Dallas, Philadelphia, Portland, Tucson, Des Moines, Las Vegas, Boston

Houston, Kansas City, Minneapolis, Sacramento, Detroit, Salt Lake City, Baltimore, Colorado, Springs, Jacksonville, Little Rock, Los Angeles, Raleigh,

Durham, Washington D.C in United Sates; Calgary, Edmonton, Montreal, Toronto, Vancouver, Winnipeg in Canada; London, Paris, Amsterdam, Berlin,

Essen, Stockholm, Barcelona, Rome, Madrid, Oslo-Blindern, Prague in Europe; Tokyo, Osaka, Hiroshima in Japan; Bankstown, Brisbane Aero, Melbourne

in Australia.

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HUANG ET AL.

written by banks, insurance companies, brokers, hedge funds, and other financial companies, tailored to specific end-user. In

practice, these OTC contracts can be written for any location or group of locations and for any measurable weather index.

Because of the variability of weather risk, weather derivatives have been structured to cover almost any type of weather

variable: temperature, rainfall, snowfall, wind speed, and humidity, for example. According to the recent survey of the weather

derivatives market by Weather Risk Management Association (WRMA, 2011a), the CME where weather contracts are largely

dominated by temperature-based index has shown that weather risk contracts account for 98%. In addition, weather derivative

deals can be structured to refer to maximum, minimum, or daily average temperatures. For example, heating degree days (HDD)

and cooling degree days (CDD), defined on the basis of daily average temperatures, are two common derivatives. A company can

buy a CDD during the summer or HDD for winter to hedge weather risk. The energy sector is the primary user of weather

derivatives (Alaton et al., 2002; Cao & Wei, 2004), though abnormal climates have led to steady growth in the market too.

According to the WRMA (2011b) survey report, the weather derivatives market grew by 20% and the total notional value for

OTC traded contracts rose to $2.4 billion in 2010–2011, while the overall market grew to $11.8 billion. Weather derivatives thus

have gained popularity as tools to manage weather risk.

Even as weather derivatives become more important, no standardized model exists to capture weather dynamics, nor is there

any effective valuation method for weather derivatives. For example, several considerations make pricing temperature

derivatives more difficult than pricing traditional derivatives (Alaton et al., 2002; Brody et al., 2002; Campbell & Diebold, 2005;

Cao & Wei, 2004; Groll et al., 2016; Hardle & Lopez Cabrera, 2012; Huang et al., 2008; Zapranis & Alexandridis, 2009). First,

modeling underlying temperature indices is essential to price derivatives but also is challenging, because temperature is highly

localized and consists of different features. Second, underlying temperature indices are not tradable and cannot be derived from a

no-arbitrage condition, because it is not possible to replicate the payoff of a given contingent claim by a controlled portfolio of

basic securities. Third, the liquidity of temperature derivative markets has improved, but they still are not as complete as

traditional derivative markets. In turn, we cannot apply a classic Black–Scholes–Merton methodology. Instead, we confront the

challenge of developing a temperature forecasting model that can be integrated into an options pricing framework, while also

providing accurate estimates and forecasts.

To date, a variety of temperature behaviors have been addressed and the corresponding temperature model is proposed to

govern its temperature behavior. Alaton et al. (2002) construct a temperature model that accounts for global warming,

seasonality, and mean reversion, and then they derive the closed-form pricing formula for the weather derivative. Huang et al.

(2008) extend their work to consider volatility clustering and incorporate a GARCH process with temperature. For both HDD

and CDD, the call price is higher with ARCH effects variance than fixed variance. In addition, Cao and Wei (2004) model the

dynamics of temperature by considering seasonal variation, mean reversion, volatility clustering, a larger variation in daily

temperature in winter than in summer, and global warming. Campbell and Diebold (2005) time-series approach captures and

forecasts daily average temperature features, in line with Cao and Wei (2004), but also considers both the conditional mean and

conditional variance in daily temperature behavior, constructing a future distribution of underlying temperature indices. Benth

and Saltyte-Benth (2007) propose an Ornstein–Uhlenbech process with seasonal volatility to model the time dynamics of daily

average temperatures and pricing HDD and CDD futures and options. They show that HDD futures curve gives higher prices

when taking into account the seasonal volatility of temperature compared with a constant volatility. Thus prior literature denotes

the temperature properties of global warming, seasonality, mean reversion, volatility clustering, and seasonal cyclical in

volatility to model temperature.

Another important feature is that temperature variability may exert a long memory effect (Benth, 2003; Brody et al., 2002;

Caballero et al., 2002; Syroka & Toumi, 2001; Tsonis et al., 1999). This long memory arises from the presence of positive long-

range correlations or persistence in temperature data. If an anomaly with a particular sign exists in the past, it likely persists in the

future. Existing research suggests two ways to identify the long memory effects for temperature. First, Syroka and Toumi (2001)

use a simple method to identify the presence of long-range dependence in temperature data. Brody et al. (2002) apply their

method to test for long memory, but whereas Syroka and Toumi (2001) rely on fractional Brownian motion to model temperature

dynamics, Brody et al. (2002) propose a fractional Ornstein–Uhlenbeck process to price HDD and CDD contracts using partial

differentials. Second, Caballero et al. (2002) use an econometric approach, focusing on long memory effects with conditional

mean dynamics of temperature and employing autoregressive fractionally integrated moving average (ARFIMA) models to

reflect temperature dynamics. They find that the long memory model from ARFIMA provides more accurate pricing results than

the short memory version. Benth (2003) also considers the effect of long memory in temperature evolution, together with a mean

reversion toward seasonal variation, though without any empirical test. With the assumption that temperature follows a fractional

Ornstein–Uhlenbeck process, he uses an arbitrage-free method to price dynamics for claims on temperature. Schiller et al. (2012)

proposed the splines model to separate the daily temperature data into trend and seasonality component. Further, they model the