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Indian Journal of Finance and Banking; Vol. 4, No. 2; 2020 
                                       ISSN 2574-6081   E-ISSN 2574-609X 

Published by CRIBFB, USA 

38 

 

Evaluating Rainfall Risk Profile of Indian Subcontinent Based on Index 
Metrics 

  

 
Bharath V PhD 
Research Scholar 

DoS in Commerce 
University of Mysore, Mysuru, Karnataka, India 
E-mail: bharathv@commerce.uni-mysore.ac.in 

 
Kotreshwar G PhD 

Professor (Rtd.) 
Senior Fellow, ICSSR, New Delhi, India 

E-mail: kotreshwar@commerce.uni-mysore.ac.in 
 
 
Received: July 09, 2020       Accepted: July 20, 2020     Online Published: August 09, 2020 
 
doi: 10.46281/ijfb.v4i2.700        URL: https://doi.org/10.46281/ijfb.v4i2.700 
 
 
Abstract 
Floods and droughts represent an embedded monsoon factor impacting the Indian economy. Evaluating monsoon risk based 
on rainfall index metrics could help design appropriate alternative risk transfer products.  This study proposes a new set of 
rainfall indices that can be used to explore the excess rainfall risk profile of the Indian Subcontinent. The study proposed a 
new set of indices for evaluating excess rainfall risk profiles which are defined as Excess Rainfall Days (ERDs). The 
methodology proceeds in a step-wise form: Empirical values of ERDs over 50 years for selected MSDs of India are derived, 
and then these index values are analyzed for determining the degree of variability and volatility, followed by the examination 
of the degree of inter-correlation amongst indices of selected Meteorological Sub-divisions. The research is based on the 
applications of econometric models such as the Augmented Dickey-Fuller (ADF) test followed by the GARCH model. The 
results revealed that several of the statistical properties of ERD indices support the idea that these indices could be used as 
building blocks for designing rainfall derivatives similar to HDDs/CDDs underlying temperature derivatives. 
 
Keywords: Rainfall Indexation, Floods, Excess Rainfall Days (Erds), Rainfall Derivatives.         
 
JEL Classification Codes: F37, G19, G29, G22, Q59.                 
 
1. Introduction  
India is exposed to a wide range of weather-related risks such as droughts, floods, storms, landslides, and extreme 
temperatures. India‟s economic losses from weather-related events have doubled over the last thirty years (Singh, Del Rio, 
Soundarajan, Nath, & Shivaranjani, 2018). A report of McKinsey Global Institute has found that economic damage 
incurred by Mumbai (India) from flash floods could be almost double by 2050. Therefore, Floods are the most 
economically damaging weather-related events, costing more than all other disaster events combined. From 1998 to 2017, 
10 out of 14 extreme weather-related disasters were floods, causing economic damage of approximately US $45 billion and 
killing over 27000 people and affecting more than 370 million people (Singh et al., 2018) in India. Therefore, Effective 
management of excess rainfall risk is essential for achieving sustainable development of the economy. Traditional risk 
management tools like crop insurance programs are found to be grossly inadequate. A recent innovation in the financial 
markets involves the development of a rainfall-index based on derivative products as a risk management tool to hedge excess 
rainfall. Rainfall derivatives (RDs) represent new alternative risk transfer tools that could be used in the capital market to 
minimize the adverse impact of floods on the Indian economy. India has well-developed financial markets and it has been 
experiencing hassle-free trading from the past two decades. Even the Securities and Exchange Board of India (SEBI) has 
actively been considering a proposal to allow trading in weather derivatives. Therefore, India too needs such derivative 
products, as investors are more mature now, this product would be a game-changer for many stakeholders. This study 
introduces a new set of rainfall indices that can be used as building blocks for designing rainfall derivatives contracts.   

The proposed study aims to determine rainfall indices for selected Meteorological Sub-divisions (MSDs) of India 
based on a new methodology. The Statistical properties of computed indices will be analyzed to assess the rainfall risk 
profile. The study also intends to examine the relationship of rainfall Indices among the selected Meteorological Sub-
divisions of India. 

mailto:bharathv@commerce.uni-mysore.ac.in
mailto:kotreshwar@commerce.uni-mysore.ac.in
https://doi.org/10.46281/ijfb.v4i2.700


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39 

 

2. Floods in India   
Most of the losses faced by India are due to an increase in flood events and cyclones, which are projected to increase in 
magnitude and frequency in the near future. Hence, India has high exposure to weather-related events. In 2018, a prolonged 
southwest monsoon over the state of Kerala resulted in one of the worst floods in 100 years, causing estimated losses of US 
$4.25 billion. Over 8 lakh people were displaced and 400 lives lost over a span of 2 weeks (Chacko, Ranadive,  Sachdeva, 
Hede, Bhati, Nainan, & Jagasheth, 2018). In 2019, many states across the country have witnessed severe drought 
conditions, followed by a delayed monsoon, which was made up for by spells of high-intensity rainfall resulting in heavy 
flooding across the country. Therefore, Indian summer monsoon volatility could adversely impact agriculture, water 
resources, power generation, and the overall economy (Mooley, Parthasarathy, Sontakke, & Munot, 1981; Mooley & 
Parthasarathy, 1983; Parthasarathy, Munot, & Kothawale, 1994). Kumar and Parikh (2001) found that there was a strong 
relationship between agricultural performance and climate; and there will be a significant loss in net revenue due to global 
warming. However, drought impacts less frequently in some areas of India, floods cause severe damage to livelihood and 
agriculture in other areas; one-third of the average flood-prone area in the country constitutes agricultural land (IPCC, 
1995).  
 

 
 

Figure 1. Total crops damages due to floods in India from 1970-2017 
 

Source: Flood Damage Statistics Report, Central Water Commission, Government of India (2019) 
  

Figure 1 shows the year-wise total crop damage due to floods from 1970 to 2017. From 1970 to 2017, India 
suffered damages due to floods and heavy rains. The year 2015 was the most catastrophic for India. The data from the 
Central Water Commission show the country‟s total crop loss due to floods in 2015 was Rs. 17043.98 Crore. Moreover, 
crop damage due to floods and heavy rainfall has increased exponentially in the last two decades (Figure 1). 

India is among the countries most affected by weather-related risk. Most of the studies have found that floods will 
become more frequent in India. CWC report shows the year-wise area affected due to floods. It shows that the area affected 
by floods in India does not follow any pattern. The lowest area affected by floods in India was 1.09 million hectares in 
2006 and the highest was in 1978 with an area of 17.5 million hectares. The most recent and devastating example was 
2013 in Kedarnath, 2015 in Chennai, 2018 in Kerala, 2019 in Karnataka and Maharashtra.  According to the Central 
Water Commission report on state-wise flood damage statistics show that West Bengal was the highest damage to crop due 
to floods and heavy rain followed by Andhra Pradesh, Karnataka, Uttarakhand, Uttara Pradesh, Kerala, and Arunachal 
Pradesh.  
 
3. Rainfall Derivatives  
Developments in global financial markets provide unique opportunities for managing catastrophic risks. The two promising 
innovations that could provide for effective management of monsoon risk are (1) Index-based insurance contracts and (2) 
Rainfall derivatives. Index-based insurance is an alternative form of insurance that makes payments based not on measures 
of farm yields, but rather on some objective weather event such as rainfall. Agricultural insurance is an industry that is still 
in its evolution stages in India. Rainfall index (RI) insurance introduced by leading insurance companies in India in the 
recent past holds better prospects over traditional crop insurance. The development of RI insurance just marks the 
beginning of a journey towards the creation of full-fledged rainfall markets for absorbing monsoon risk to meet the hedging 
needs of a wide range of stakeholders including agri-insurers, agri-finance companies, commodity trading enterprises, hydro-
power utilities, agro-processing companies, etc. Designing such a derivative requires determination of rainfall index metrics 

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40 

 

which could be used as building blocks. In 2011 Chicago Mercantile Exchange (CME) pioneered trading rainfall futures 
and options on monthly and seasonal rainfall indices.  
 
4. Research Questions 

 What should be the framework for the standardization of measures of rainfall indices for quantifying excess 
rainfall risk? 

 What should be the approach for deriving empirical values of excess rainfall indices of Meteorological Sub-
divisions of India? 

 What are the statistical properties of the empirical values of excess rainfall indices? 

5. Research Methodology 
The following methodology is adapted to analyze the rainfall time series data. The research is based on the applications of 
econometric models such as the Augmented Dickey-Fuller(ADF) test followed by the GARCH model. 
 
5.1 Study Area 
The high intensive monsoon rain and melting of Himalayan glaciers is a major source of flood in India.  According to 
Central Water Commission (CWC) report on state-wise flood damage statistics show that West Bengal has the highest 
damage to crop due to floods and heavy rain followed by Andhra Pradesh, Karnataka, Uttrakhand, Uttar Pradesh, Kerala, 
Arunachal Pradesh, Gujarat region and Saurashtra region. The sample consists of the top 10 floods damaged 
Meteorological Sub-division of India based on the Central Water Commission Report.  
 
5.2 Data and Methodology 
A standard methodology for rainfall indexation is yet to emerge. Stoppa and Hess (2003) developed a rainfall index on 
several aggregated weights of average rainfall in ten-day periods in each growth stage. National Commodity Derivative 
Exchange (NCDEX) proposed a rainfall index based on historical cumulative rainfall. First Rainfall Index for Mumbai city 
was launched in 2005. Rainfall Index (RI) for a stated location is determined as: 

RI location = 
 𝑟𝑖𝑡

 𝑅𝑖𝑡
𝑋 𝑠𝑐𝑎𝑙𝑒 𝑣𝑎𝑙𝑢𝑒        (1) 

 
        Where rit represents actual rainfall of ith day of the tth season; Rt represents long period average daily rainfall of ith 

day of the tth season; scale or multiplier value was assumed 1000 (rainfall is measured equivalent to 1/1000 th of a met, i.e., in 
millimeter). RI location indicates what percentage of cumulative normal expected rainfall is realized, which means a higher the 
rainfall index value meaning that compared to the cumulative average rainfall up to the date of an index, there has been more 
rainfall. 
    Similarly, in 2005, Multi Commodity Exchange (MCX) and Weather Risk Management Services Pvt. Ltd. jointly 
developed rainfall indices based on historical annual cumulative rainfall and it adjusted with excess and deficit of actual 
cumulative rainfall as of that data. The adjustment factor takes into account the impact of historical and actual rainfall 
during the period.  

Kotreshwar (2006), Kotreshwar & Kanakasabai, (2006), Kotreshwar & Arunkumar (2006), Shivkumar & 
Kotreshwar (2013), Kotreshwar (2015) proposed process of rainfall indices based on a ticker value defined as Monsoon 
Outcome Index (MOX) and estimated their statistical properties of MOX series across time and subdivisions, and the 
study examined the potential of MOX as a new asset class for inclusion in the portfolio for risk hedging.  

Later, Kotreshwar (2015) has modified their suggested methodology to compute rainfall indices as Deficit 
Rainfall Days (DRDs) and Excess Rainfall Days (ERDs). This approach appears to be more relevant to define and evaluate 
rainfall variability using DRD/ERD measures as standard metrics.  The present study is based on this new approach for 
rainfall indexation.  

Two important characteristics within the rainfall time series are highly skewed and volatility clustering. A series 
with some periods of low volatility and some periods of high volatility is said to exhibit volatility clustering. Volatility 
clustering can be thought of as clustering of the variance of the error term over time that is if the regression error has a small 
variance in one period; its variance tends to be small in the next period, too. In other words, volatility clustering implies  that 
the error exhibits time-varying heteroscedasticity, that is, unconditional standard deviations are not constant. These 
characteristics can be captured by the GARCH family models. 

The residuals can be modeled with ARCH dynamics. The conditional variance allows for two types of volatility 
dynamics that are relevant in rainfall. They include seasonal volatility and autoregression effects in which shocks to the 
conditional variance may have effects that persist for several periods. Campbell and Diebold (2005) use an autoregressive 
moving average (ARMA) time series model for temperature and observe seasonality in the autocorrelation function for the 
(squared) residuals when modeling the temperature in US cities. They propose a seasonal autoregressive conditional 
heteroskedastic (ARCH) process to model volatility. A similar method adopted by Anastasiadou and López-Cabrera 
(2013) proposed a GARCH model to identify volatility in weather indices.  
 
 



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5.3 Methodology  
Excess rainfall at a given location needs to be quantified using a standard metric. For this purpose, the historical daily 
average rainfall for the selected location would serve as the „base‟ rainfall for calculating the metric. Rainfall at a locat ion 
equivalent to being above a defined normal rainfall by one millimeter for one day can be denoted „Excess Rainfall Day‟ 
(ERD). For example, given the historical daily average rainfall for June for a location is 3 mm and if the actual daily average 
rainfall is 5 mm, we can approximate the ERD for June as 60 (2 x 30 days). A South-West monsoon season of 4 months 
(June-Sept) might accumulate a seasonal minimum of zero or a maximum of over 100 ERD for a location. A zero ERD 
means that all the four months recorded deficit rainfall.  

The underlying variable being rainfall, let Ri denote the rainfall (in millimeters) measured on ith day, and Rx 

denotes the average daily rainfall (in millimeters).  The average daily rainfall, Rx, should serve as the reference level of 
rainfall in millimeters. The value of Rx is based on the past rainfall data for any chosen length of the period. The standard 
underlying variable, then, would be simply the difference between the daily average value of rainfall (in millimeters), i.e., Rx 

and the actual value of rainfall (in millimeters) on ith day, i.e., Ri. The ERD generated on a given ith day then is given by: 

 ERDi = Max. {Ri – Rx, 0}                                               (2) 

In equation (2) above, it can be seen that the number of ERD for a specific day is just the number of millimeters 
that the rainfall deviates from a reference level. The methodology adopted in this paper comprises the following steps: 

 Estimation of reference level of rainfall for each of the selected meteorological sub-divisions(MSDs) of India  

 Estimating the ERD for each month of the south-west monsoon  

 Taking the sum of ERD for all the four months   

The number of accumulated ERD (En) for a period of „n‟ days can be determined as follows: 

             𝐸𝑛 =  𝐸𝑅𝐷𝑖
𝑛
𝑖=1                                                   (3) 

 
Monthly ERD facilitates to capture the element of variability in each month of the south-west monsoon. The 

values of ERD based on equations (2) & (3) for the selected 10 of the 36 MSDs of India are determined for each of the 50 
years from 1970-2019 (Appendix-1). The sample data is drawn from the official website of the Indian Meteorological 
Department (IMD) of India. 

The study is based on secondary data. The rainfall data is collected from the India Meteorological Department 
(IMD). The study covered monthly average rainfall data of the south-west monsoon season (June to September) for the 
analysis. The study covers the past 50 years (1970 to 2019) rainfall data of selected 10 of the 36 Meteorological 
subdivisions of India is considered.  

 
5.4 Statistical Tests 
The homogeneity test is to test whether a given data is said to be homogenous over time. In other words, if there is a 
significant break in the trend of particular time series it is classified as inhomogeneous. This inhomogeneity in historical 
data will impact the outcome of data analysis and forecasts. Hence, it is important to test the homogeneity of the rainfall 
data series by applying four methods Pettitt, SNHT test, Buishand, and Von Neumann test. 

Most of the statistical procedures including correlation, regression, and analysis of variance are parametric tests. 
These parametric tests are based on the assumption that the data follows a normal distribution. To test the normality of the 
data series Shapiro-Wilk test and Jarque-Bera test have been applied. The null hypothesis is that sample distribution is 
normal. If the computed p-value is lower than the significance level alpha=0.05, it is indicated that the data series is not 
normally distributed.  

Augmented Dickey-Fuller (ADF) test suggested by Dickey and Fuller (1979, 1981) is applied for the null 

hypothesis that a series (Yt) is non-stationarity by calculating at-statistics for 𝛽 = 0 in the following equation: 

                      ∆𝑌𝑡 =  𝛼1 + 𝛽𝑌𝑡−1 + 𝛾𝑡 +  𝛿𝑘   ∆𝑌𝑡−𝑘 + 휀𝑡
𝑛
𝑡−1    (4) 

           Where k =2,3,…..n. while,𝛼,𝛽,𝛾, 𝑎𝑛𝑑 𝛿 are the parameters to be estimated and 𝜺𝒕 is a white noise error term. 
If the value of the ADF statistic is less than the critical value at the conventional significance level (usually at 5% 
significance level) then the series (Yt) is said to be stationary and vice versa. If (Yt) is found to be non-stationary then it 

should be determined whether (Yt) is stationary at first differences ∆Yt - I(0) by repeating the above procedure. The first 
difference of the series is stationary then the series (Yt) may be concluded as integrated of order one i.e.Yt - I(0). 

To analyze the existence of autocorrelation, if any, the following autocorrelation function (ACF) for rainfall time series 𝑟𝑡  is 
applied: 

                  Corr (𝑟𝑡 ,𝑟𝑡−𝑘),𝑘 = 1,2… . . 𝑛                        (5) 

            Where the value of k is the time gap is considered. A lag 1 autocorrelation (i.e,., k=1 in the above) is the 
correlation between values that are one time period apart. The ACF is a way to measure the linear relationship between an 



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observation at time t and the observations at previous times. If the coefficient of correlation falls between the upper and 
lower limits of a confidence interval, then the data is considered auto correlated.  

          To analyze the variability of rainfall amongst meteorological subdivisions, the GARCH model has been applied. 
Under GARCH (Bollerslev, 1986) model the forecasts of time-varying variance depend on the lagged variance of any asset. 
This GARCH (1,1) can be expressed as; 

𝜎𝑡
2 = 𝑘 + 𝛼

𝑝
𝑖=1 𝜖𝑡−1

2 +  𝛽
𝑞
𝑗=1 𝜎𝑡−1

2  + 𝜖𝑡               (6) 

 

Where the conditional volatility (𝜎𝑡
2) is specified in the above model is determined by three effects namely, k is a 

constant term, 𝛼 ∈𝑡−1
2 indicates yesterday‟s news about volatility illustrated by the ARCH term, and 𝛽 𝜎𝑡−1

2 explains the 

forecasted volatility from the previous period called as GARCH component, 𝜖𝑡  is the error term. P is the degree of ARCH 

term and Q is the degree of GARCH term. The parameters α and β define as short-run dynamics of the resulting volatility 
time series. The coefficient is close to the one we assume that there is a high persistence of volatility. 

 
6. Results and Discussion  
The preliminary analysis for this study included computing statistical parameters like mean, median, maximum, minimum, 
standard deviation, skewness, and kurtosis for Excess Rainfall Days (ERD) in the South-west rainfall series of selected 
Meteorological sub-divisions for 50 years the period from 1970 to 2019 as shown in Table-1. 
 
Table 1.  Summary of descriptive statistics of ERD values of selected MSDs in India 
 

Regions Sub-divisions Mean Median Maximum Minimum SD Skewness Kurtosis 

North HIMACHAL PRADESH 110.86 106.03 472.90 0.00 107.90 1.02 4.12 

UTTARANCHAL 156.70 138.50 673.00 0.00 153.24 1.32 4.56 

WEST UP 122.51 131.00 443.88 0.00 104.46 0.71 3.44 

South COSTAL AP  81.65 75.58 272.8 0.00 75.02 0.79 2.76 

SOUTH INTERIOR 
KAR  

85.59 78.08 239.57 0.00 68.41 0.42 2.14 

East BIHAR 138.07 153 553.7 0.00 111.58 1.19 5.34 

GANGETIC WB  152.82 141.38 465.88 0.00 127.85 0.59 2.41 

ODISHA 124.04 99.00 483.00 0.00 121.02 1.39 4.55 

West GUJRAT 198.51 159.00 663.52 0.00 171.42 0.91 3.19 

SAURASHTRA 161.94 104.54 1173.47 0.00 197.89 2.94 14.86 

Source: E-views output of the data sourced from IMD reports -1970 to 2019 
  

        The mean of Excess Rainfall Days (ERDs) values is highest in the west region followed by East and North. The 
highest and lowest mean values are 198.51and 81.65 for Gujarat and Coastal Andhra Pradesh respectively. It is observed 
that mean values in the ERD are different in all subdivisions. The maximum ERD value is in the West region followed by 
the North and East regions. Saurashtra region (1173.47) has the highest ERD values and the lowest is in South Interior 
Karnataka (239.57). The standard deviation method is used to measure the volatility in the ERD values. West region has 
the highest volatility in the ERD values followed by the east and north region. Moreover, the South region has the lowest 
standard deviation values. Saurashtra (197.89) has the highest volatility among the selected MSDs while south interior 
Karnataka(68.1) has the lowest.  

The rainfall derivatives contracts payoff is based on an underlying index (ERD) which is observed from rainfall 
data at a specific geographic location. Based on this, the mean ERDs values for the selected regions would serve as the 'base' 
for calculating the payoff of the contract. For example, from the above table-1, the mean ERDs values of south-west 
monsoon season for Gujarat were 198.51 mm, this value indicates that every year Gujarat has been facing a minimum of 
193.84 mm of excess rainfall from the south-west monsoon season. These ERDs values of the Gujarat region would serve a 
benchmark for designing rainfall options and futures contracts for trading in the markets. 

Skewness is a measure of the abnormality of the distribution of the data series around its mean. All sub-divisions 
were positively skewed, which means the distribution has a long right tail. Kurtosis measures the flatness or peakedness of 
the data series. Out of 10 sub-divisions, the Kurtosis value of 3 sub-divisions was less than 3, indicating that the 
distribution is flat (platykurtic) relative to the normal. Seven sub-divisions have a kurtosis value of more than 3; the 
distribution is peaked (leptokurtic) relative to the normal. 

 
 
 
 



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  Table 2.  Summary of Homogeneity test 
 

Regions Sub-divisions Pettitt SNHT 
test 

Buishand   von   
Neumann 

North HIMACHAL  
PRADESH 

0.258 0.431 0.230 0.239 

UTTARANCHAL     

WEST UP 0.082 0.111 0.046 0.874 

South COSTAL ANDHRA  
PRADESH  

0.892 0.641 0.364 0.916 

SOUTH INTERIOR 
KARNATAKA  

0.222 0.391 0.896 0.675 

East BIHAR 0.359 0.330 0.291 0.276 

GANGETIC WEST  
BENGAL  

0.406 0.453 0.341 0.339 

ODISHA 0.838 0.491 0.258 0.297 

West GUJRAT REGION 0.328 0.521 0.726 0.057 

SAURASHTRA 0.066 0.019 0.073 0.034 

Note: Tested at 5% significance level. 
Source: E-views output of the data sourced from IMD reports -1970 to 2019 

 
The results of the homogeneity test of ERD values have been tested using Pettitt, SNHT test, Buishand, and von 

Neumann test. If an ERD series may be considered as homogeneous over time, or if there are some years at which a change 
occurs. The null hypothesis is that a time series is homogenous between two given times. The above results indicating that 
all the MSDs follow homogeneously. As the computed p-value is greater than the significance level alpha=0.05, one cannot 
reject the null hypothesis. Therefore, the ERD values considered as homogenous over time. 
 
Table 3. Result of the stationary test from Augmented Dickey-fuller test (ADF) test  
 

Regions Sub-divisions    Level  Data  1st    
Difference 

    Order Decision 

North HIMACHAL PRADESH 0.0000** - I(0) Stationary at level 

UTTARANCHAL 0.1412 0.0000** I(1) Stationary at difference 

WEST UP 0.3433 0.0000** I(1) Stationary at difference 

South COSTAL ANDHRA  
PRADESH  

0.0052** - I(0) Stationary at level 

SOUTH INTERIOR 
KARNATAKA  

0.0000** - I(0) Stationary at level 

East BIHAR 0.0000** - I(0) Stationary at level 

GANGETIC WEST  
BENGAL  

0.0000** - I(0) Stationary at level 

ODISHA 0.0000** - I(0) Stationary at level 

West GUJRAT REGION 0.0000** - I(0) Stationary at level 

SAURASHTRA 0.0003** - I(0) Stationary at level 

Note **denote rejection of the hypothesis at a 5% significance level. 
Source: E-views output of the data sourced from IMD reports -1970 to 2019 

 

Table 3 shows the stationary test of selected metrological sub-divisions of India. Rainfall series is said to be 
stationary if the mean and variance of the series do not change over time, significance that stationery can be defined as no 
trend, constant variance over time, and no seasonality in the data series. To identify the stationarity in the rainfall series, 
Augmented-Dickey Fuller (ADF) test has been applied. The results display that South, West, and East regions are 
stationary at level data, only North sub-divisions are stationary at first difference. South, West, and East region series are 
stationary, indicating that these regions ERD values have no trend and no seasonality in the series. North region is non-
stationarity at level data, indicating that North region ERD values have long-term trend and seasonality (fluctuations) in 
series.  
 

 
 



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Table 4. Results of Normality Test 
 

Regions Sub-divisions Shapiro-Wilk Jarque-Bera 

North HIMACHAL PRADESH 0.000 0.003 

UTTARACHAL <0.0001 <0.0001 

WEST UP 0.001 0.095 

South COSTAL ANDHRA  
PRADESH  

0.001 0.069 

SOUTH INTERIOR 
KARNATAKA  

0.006 0.216 

East BIHAR 0.001 <0.0001 

GANGETIC WEST  
BENGAL  

0.004 0.162 

ODISHA <0.0001 <0.0001 

West GUJRAT REGION 0.001 0.029 

SAURASHTRA <0.0001 <0.0001 

                                            Note: Tested at 5% significance level. 
Source: SPSS output of the data sourced from IMD reports -1970 to 2019 

 
Several statistical methods can be used to identify the normal distribution. The results of the normality of ERD 

values have been tested using Shapiro-Wilk and Jarque-Bera test. Table4 shows that all the MSDs do not follow a normal 
distribution. As the computed p-value is lower than the significance level alpha=0.05, it is observed that the ERD values of 
selected sub-divisions are not normally distributed, and hence, the non-parametric test can be used for further analysis. 

  
Table 5. Results of Autocorrelation Function (ACF) of selected MSDs of India 
 

 North South East West 

Lags 
(k) 

Himachal 
Pradesh 

Uttaranch
al 

West UP Costal 
AP 

SIK Bihar Gangetic 
WB 

Odisha Gujrat Saurasht
ra 

1.  0.095 -0.491 -0.635 -0.193 -0.120 0.064 0.039 0.066 0.187 -0.011 

2.  0.151 -0.161 0.106 0.001 0.020 0.013 -0.132 0.057 -0.024 0.065 

3.  -0.001 0.406 0.237 0.046 -0.141 0.230 -0.109 -0.046 0.053 -0.032 

4.  -0.116 -0.318 -0.473 -0.377 -0.120 -0.004 -0.006 -0.131 -0.067 0.028 

5.  0.020 0.024 0.494 0.242 -0.007 -0.155 -0.205 0.094 -0.217 -0.115 

6.  -0.039 0.034 -0.339 -0.218 0.135 -0.004 0.149 -0.080 -0.080 0.046 

7.  0.161 0.084 0.043 0.100 -0.150 -0.181 0.090 0.123 0.032 -0.105 

8.  0.202 -0.047 0.242 0.095 0.110 0.031 -0.050 -0.089 -0.077 0.005 

9.  -0.027 -0.100 -0.386 0.076 -0.035 -0.007 0.113 -0.130 -0.134 0.252 

10.  0.064 0.215 0.344 0.124 -0.001 -0.025 -0.074 -0.137 -0.124 0.014 

11.  -0.189 -0.149 -0.146 -0.144 -0.062 -0.001 -0.004 -0.080 -0.007 -0.034 

12.  -0.196 0.040 -0.087 0.155 -0.105 0.016 0.077 0.203 -0.059 0.033 

13.  -0.181 0.014 0.231 -0.098 0.108 0.026 0.002 0.124 0.073 0.095 

14.  -0.222 -0.138 -0.265 -0.018 0.045 -0.041 -0.119 0.053 0.003 0.045 

15.  0.068 0.129 0.282 -0.048 -0.077 -0.211 0.070 0.002 0.004 0.020 

Note: Tested at 5% significance level. 
Source: E-views output of the data sourced from IMD reports -1970 to 2019 

 
 

 
 
 
 
 
 
 
 
 
 



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North Region                                                   South Region  
 

                        Himachal                           South 
          Pradesh               Uttaranchal              West UP                 Costal AP           Interior  Kar 

 
 
                              East Region                                         West region 
 
           Bihar                Gangetic WB              Odisha                         Gujarat              Saurashtra 

 
 
 

Figure 2.  Autocorrelation Function (ACF) plot of ERD values 
Source: E-views output 

 
The Autocorrelation Function (ACF) Figure 2 illustrates the correlation of the ERD series at various lags. The 

lag refers to the order of correlation. Each spike that rises above or falls below the dashed lines is considered to be 
statistically significant. This means the spike has a value that is significantly different from zero. If a spike is significantly 
different from zero, which is the evidence of autocorrelation. If a spike that is close to zero is the evidence of no 
autocorrelation in the series.  

The ACF plots show that 7out of 10 sub-divisions are not statistically significant and within the 95% confidence 
interval. This indicating that there is no autocorrelation in the ERD values. The ERD values of these sub-divisions tend to 
fluctuate randomly around zero and they are independent of each lag. ACF plot of Uttaranchal, West UP, and Coastal 
Andhra Pradesh are statistically significant. This indicates that the ERD values have strong autocorrelation and they are 
dependent on each lag. 

 

 

 



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Table 6.The results of the GARCH model 
 

Regions Sub-divisions α 𝛃 GARCH(1,1) 

(α+β) 

P-value Volatility  

North HIMACHAL  
PRADESH 

-0.0769 0.7985 0.7216 0.0329 High  

UTTARANCHAL 0.4522 0.3545 0.8067 0.1477 High  

WEST UP 0.4330 -0.0524 0.3806 0.9515 Low  

South COSTAL ANDHRA  
PRADESH  

-0.3380 1.2847 0.9467 0.0000 High  

SOUTH INTERIOR 
KARNATAKA  

-0.4369 1.3366 0.9066 0.0000 High  

East BIHAR -0.3059 1.3135 1.0076 0.0005 High  

GANGETIC WEST  
BENGAL  

-0.3671 1.3222 0.9551 0.0000 High 

ODISHA -0.3787 1.4042 1.0255 0.0000 High 

West GUJRAT REGION -0.2425 1.1717 0.9292 0.0000 High  

SAURASHTRA -0.4583 1.3265 0.8682 0.0000 High  

Note: Tested at a 5% significance level. 
Source: E-views output of the data sourced from IMD reports -1970 to 2019 

 

      The results of GARCH models are reported in Table 6. GARCH model is used to test the volatility in the ERD 

series in selected MSDs of India. Table 6 represents two coefficients are α and β indicating the estimated ARCH and 
GARCH coefficients. This coefficient is a measure of the persistence of volatility. The coefficient value is close to 1(one) 
which indicates a high persistence of volatility in the ERD values. The results indicating that all 10 subdivisions have high 

volatility expect West UP. It is observed that the sum of ARCH and GARCH coefficients (α+β) is very close to 1(one) 
for all selected MSDs expect West UP sub-division as the computed p-value is lesser than the significance level alpha=0.05. 
Therefore, the study concludes that the selected subdivisions have high volatility persistence levels in the ERD values.  
 
Table 7. Results of the Correlations matrix among selected MSDs. 
 

Spearman's rho Correlation Coefficient Sig. (2-tailed) 

 Gangetic 
WB 

Bihar West UP Uttaranchal Odisha Gujarat 
Region 

Saurashtra Himachal 
Pradesh 

Coastal 
AP 

South 
Interior 

Kar 

Gangetic 
WB 

1          

          

Bihar .313* 1         

(0.027)          

West UP .029 -.085 1        

(0.843) (0.557)         

Uttaranch
al 

.041 -.074 .382** 1       

(0.779) (0.610) (0.006)        

Odisha -.031 -.005 .081 .091 1      

(0.830) (0.975) (0.576) (0.52)       

Gujarat 
Region 

-.060 -.064 .270 .314* .180 1     

(0.680) (0.658) (0.058) (0.026) (0.21)      

Saurashtra -.128 -.164 .061 .290* .130 .565** 1    

(0.374) (0.254) (0.673) (0.041) (0.36) (0.00)     

Himachal 
Pradesh 

.091 -.046 .488** .240 .050 .165 .240 1   

(0.528) (0.754) (0.000) (0.093) (0.73) (0.25
2) 

(0.093)    

Coastal 
AP 

-.024 .140 .110 .080 -.126 .139 .354* .197 1  

(0.868) (0.331) (0.447) (0.580) (0.38) (0.33
7) 

(0.012) (0.170)   

South -.093 .045 .039 -.051 .230 .041 .293* -.104 .304* 1 



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Interior 
Kar 

(0.520) (0.758) (0.787) (0.723) (0.10) (0.77
7) 

(0.039) (0.474) (0.032)  

**. Correlation is significant at the 0.01 level (2-tailed). 

*. Correlation is significant at the 0.05 level (2-tailed). 

Source: E-views output of the data sourced from IMD reports -1970 to 2019 
  

Table 7 depicts the degree of inter-sub division dependency in ERD values of rainfall data. The pair-wise 
correlation analysis amongst ten selected sub-divisions has been carried out. It is found that the correlation value range 
between a maximum of +0.565 and a minimum of – 0.164. The result shows that out of 45 pair-wise interrelationships, 31 
out of 45 pairs have a very weak positive correlation. The remaining 14 pairs have a negative correlation. It is observed that 
ERD values among the sub-divisions have a weak correlation. 

The majority of the inter-sub divisions have a weak (i.e., near to zero and negative) correlation with 5% and 10% 
significance value. Hence, Excess Rainfall Days (ERDs) indices across inter-Meteorological Sub-divisions are significantly 
uncorrelated. ERDs can be used as a distinct asset class. Stakeholder like agri-insurance companies, having sold rainfall-
based index insurance policies across a wide geographical area, can minimize their exposure by building a diversified 
portfolio of ERD indices. Hence, there exists a vast scope for trading ERD index-based financial derivatives for hedging 
across MSDs.  
 
7. Scope for Designing Rainfall Derivatives 
The increasing popularity of temperature-based weather derivatives in the U.S. and Europe has brightened the prospects of 
innovating with rainfall based weather derivatives, particularly in some agro-based developing economies. The Indian 
situation with monsoon is the perfect opportunity to design derivative products. The monsoon has an enormous impact on 
many enterprises, including agriculture, commodity trading, agro-processing, energy, and insurance. The stakeholders in 
these markets have the need to manage monsoon related risks through rainfall derivatives. From a boarder perspective, risk 
markets have the potential to yield additional benefits too. They can promote the integration of markets by expanding the 
horizon of asset classes for investment. From the perspective of Markowitz's mean-variance efficiency, as long as the market 
is not complete, a new asset class will always improve the risk-return trade-off (Cao & Wei, 2004). ERDs could be used as 
building blocks for designing rainfall derivatives similar to HDDs/CDDs underlying temperature derivatives. Several of the 
statistical properties of ERD indices fully support this idea. The risk underlying seasonal rainfall is indicated by the degree 
of volatility in ERD indices. The results of GARCH models have shown that all the 10 sub-divisions have volatility except 
West UP. Another interesting property of ERD indices is that indices across inter MSDs are significantly uncorrelated. 
This is particularly useful when ERDs are used as a distinct asset class, by building a diversified portfolio by such 
stakeholders like general insurance companies having sold rainfall-based index insurance policies across a wide geographical 
area.  
 
8. Conclusion  
India faces most of the losses from an increase in flood events and cyclones, which are projected to increase in magnitude 
and frequency in the near future. Hence, India has high exposure to weather-related events. In this background, the study 
aims to develop the framework of standard indexation that could serve as a basis for designing rainfall-index based insurance 
and derivatives contracts. Flood index, i.e., Excess Rainfall days (ERDs) index has been developed to measure the flood risk 
with special reference to South-West monsoon. The research is based on the applications of econometric models such as the 
Augmented Dickey-Fuller (ADF) test followed by the GARCH model. Several of the statistical properties of ERD indices 
support the idea that these indices could be used as building blocks for designing rainfall derivatives similar to 
HDDs/CDDs underlying temperature derivatives.   
 
9. Research Implications 
Research has a major implication for policymaking in the field of rainfall risk management. The research inputs of the 
study, to help the creation of the market for trading rainfall derivatives like futures and options that could be used by 
stakeholders for minimizing the exposure monsoon adverse events. The SEBI has initiated a discussion on proposing new 
standardized weather derivative products that can be used to minimize the weather-related risk in India. So, the study would 
provide some inputs to develop standard metrics for measuring excess rainfall as ERDs. This rainfall indexation would serve 
as a benchmark for designing rainfall options and futures contracts for trading both in over-the-counter and organized 
markets.  
 
10. Limitations of the Study  
The study is based upon monthly rainfall data collected from Indian Meteorological Department (IMD). Instead, if the 
rainfall data is collected on daily basis results could be more accurate.  
 
 
 



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11. Scope for Further Research 
The present study was analyzed on the statistical properties of Excess Rainy Days (ERDs) for only 10 out of 36 
Meteorological Subdivisions. Further study can also be taken to consider the statistical properties of Excess Rainy Days 
(ERDs) of all 36 Meteorological Sub-division. 
 
Acknowledgment  
The authors thank the Indian Meteorological Department (IMD) for providing cost-free rainfall data for this study. The 
authors received financial support from ICSSR, New Delhi for the research, authorship, for the publication of this article. 
 
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Appendix- A 
 

ERD values for South-west monsoon for 50 years (1970-2019) 

(For Selected Meteorological Sub-Divisions (MSDs) of India) 

 

 North South East West 

Years Himachal 
Pradesh 

Uttarachal West UP Costal 
AP 

SIK Bihar Gangetic 
WB 

Odisha Gujrt Saushtra 

1970. 149.14 44 161.92 91.11 13.2 45.07 271.01 98 523.95 304.12 

1971. 320.54 171 151.38 20.26 55.44 212.46 386.95 136 45.63 55.49 

1972. 0 28 0 7.55 25.31 0 222.86 71 0 0 

1973.1 0 103 87.73 4.76 99.76 93.27 144.55 152 337 0 

1974. 0 24 118.26 44.56 148.04 175 92.67 0 0 0 

1975. 0 250 251.38 87.39 239.57 95.64 44.42 94 353.85 150.46 

1976. 124.47 0 14.67 100.94 0 178.73 0 29 663.52 95.26 

1977. 175.24 142 245.66 0 31.47 38.87 270.45 39 417.32 86.19 

1978. 170.61 503 443.88 111.55 136.07 59.97 348.85 105 153.13 75.01 

1979. 0 0 2.46 37.36 119.44 98.87 29.82 0 153.71 538.31 

1980. 239.48 118 268.98 78.61 152.27 158.03 107.89 214 125.73 283.64 

1981. 0 127 97.21 106.34 207.21 284.23 147.55 20 178.96 108.37 

1982. 0 83 172.87 0 46.83 59.5 0 109 0 0 

1983. 4.37 136 310.58 222.05 160.44 21.64 45.06 109 249.15 240.96 

1984. 9.38 148 89.42 31.38 96.07 339.34 465.88 193 135.21 30.35 

1985. 68.7 163 141.56 5.18 33.73 218.04 47.58 201 0 0 

1986. 5.16 49 14.15 72.56 90.54 69.54 250.49 96 48.63 78.09 

1987. 0 0 0 0 0 553.7 234.23 3 0 0 

1988. 472.9 178 270.48 272.8 161.94 228.33 255.72 55 299.54 370.9 

1989. 52.23 38 27.95 188.3 68.83 224.14 146.28 137 43.66 118.94 

1990. 103.54 162 214.06 10.52 0.1 148.87 216.88 66 329.6 100.72 

1991. 27.93 0 189.07 184.01 136.16 121.33 47.85 204 124.15 0 

1992. 175.8 35 121.47 26.24 134.33 0 59.07 82 101.29 158.45 

1993. 168.44 263 194.15 0 0 190.63 267.37 100 248.64 0 

1994. 206.04 185 183.43 26.78 144.96 10.37 139.29 483 578.02 381.49 

1995. 358.7 179 159.87 100.64 32.43 128.13 303.62 9 113.35 70.35 

1996. 201.64 0 160.72 152.25 82.84 138.46 301.38 23 50.84 56.39 

1997. 234.36 0 0 136.86 107.56 192.43 161.83 123 293.63 183.74 

1998. 186.68 0 145.33 150.9 96.44 235.33 23.79 40 204.49 22.79 

1999. 107.24 0 129.4 0 73.33 223.33 327.34 44 21.73 0 

2000. 118.68 198 83.48 218.41 148.34 202.97 160.39 21 0 46.95 

2001. 145.84 205 132.61 23.11 43.01 171.97 115.62 445 178.8 79.04 

2002. 152.93 255 160.87 10.71 0 68.97 115.11 0 133.93 129.69 

2003. 269 373 358.96 89.48 0 176.53 14.92 118 362.4 248.66 

2004. 0 333 1.77 20.69 5.33 159.77 55.56 6 262.51 85.91 

2005. 158.84 376 165.06 146.24 136.63 66.16 0 201 528.12 253.14 

2006. 0 48 6.46 53.57 11.13 81.67 220.36 462 580.46 216.07 

2007. 0 509 6.35 213.97 198.47 390.1 444.22 346 315.85 361.51 

2008. 109.48 122 174.41 78.94 65 236.43 173.92 296 164.3 137.75 

2009. 69.87 12 0 0 204.14 48.56 31.25 275 78.65 241.85 

2010. 171.81 673 157.53 256.25 45.34 0 0 0 200.95 495.42 

2011. 121.37 411 86.65 49.74 6.23 150.23 320.57 122 188.2 257.52 

2012. 104.83 171 2.37 99.7 20.6 6.57 0 64 108.29 133.65 

2013. 144.87 390 158.22 7.18 148.57 20.4 78.46 108 335.82 309.49 

2014. 0 94 0 0 126.34 37.06 0 233 147.94 28.95 

2015. 16.17 35 0 118.47 60.64 12.45 276.17 30 50 121.19 

2016. 32.27 162 114.16 149.61 13.33 161.54 96.36 29 17.21 55.72 



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2017. 54.47 145 11.65 105.49 98.61 110.86 143.47 15 284.62 180.25 

2018. 227.94 141 136.93 70.89 29.03 0 0 204 13.95 30.85 

2019.  82.46 53 0 99.3 224.61 258.44 34.05 192 179.1 1173.47 

 

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