# Weather Derivatives-Pricing and Design Issue in India

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2 other derivatives). Weather contracts are based on forecasting, so the information on past weather behaviors and an understanding and an understanding of the dynamics of the environment is essential. Now here comes the toughest part as the weather derivative that can be traded will have longer maturity than the data available for forecasts. So to fit a proper distribution is the critical issue. Stephen Jewson in his paper take the weather outcomes as normally distributed and even Mark Davis in his paper tried to fit lognormal distribution which is based on normal distribution itself. They both made a good attempt and give us the base to fit the distribution for forecasting and hence pricing issue. We can use the method used by S. Jewson for estimating the index variance. There are two methods, which allow us to combine probabilistic forecasts and climatological models in such a way as to calculate accurate estimates of the distribution of the index without assuming independence between the forecast and post-forecast periods. Accurate estimates of the index distribution then allow us to calculate accurate prices for WDs. The two methods are pruning and grafting. To explain each method in detail is out of scope of our paper. Once we calculate the index variance we can use this to pricing linear and nonlinear contracts. Robert Henderson gives a simple overview of pricing theory, according to him actuarial approach to pricing can be done by Price Bid (t) = D (t, T) Offer { E (P) + F Bid (R (P, CP))} Offer Where D (t, T) is present value, E (P) is the expected payout, R (P, CP) is the risky payout, which is the function of CP- current position. Design: In order to develop WDs, the weather variable must be measurable, historical records must be adequate and available, and all parties involved in the transaction must consider such measures objective and reliable. The existence of a complex relationship between the product and the weather factor must be carefully explored. For agricultural production the relationship is not always as straightforward since differences in products, crop growth phases, soil textures, etc. have different responses to the same weather factor. Also, the more skilled and advanced the cultivating techniques, the greater the entrepreneurial influence on yields the smaller the portion of variability generated by the specific weather elements. The crucial issue for application of WDs at the agricultural production level lies in the actual presence of a clear and satisfying relationship between the weather factor and the production variable. In order to be able to be successful, the WD must be able to explain a very high portion of the variability in production, loosing otherwise its attractiveness as a hedging device. Hence appropriate identification of the relationship between production and the weather variable is very important The structure of the Weather Derivative proposed in the world bank feasibility study is that of a European put option, where the option price is the cost of the derivative for the producer and the strike is the rainfall threshold below which an indemnity is triggered. 19

3 As mentioned above in designing a weather derivative for hedging weather risk at the production level, particular attention must be placed in capturing the relationship between weather factors and the specific product. In trying to address yields variability through a rainfall weather derivative the working hypothesis is that rainfall is the main determinant of crop yield and that drought is the quasi-exclusive source of risk. In this framework, the objective of the design phase is to capture the rainfall yield relationship is the most accurate way possible. The optimization problem adopted in order to select index weights can be described as follows. Effective rainfall in period i is defined as r i = max [r i *, CAP i ] (1) where r i * is actual rainfall in period i, CAP i is amount of rainfall in period I beyond which additional rainfall does not contribute to increased yield. The rainfall index for year t is defined as a weighted average effective rainfall m R t = w i r it (2) i=1 Where m is the total number of period in growing season, w i is the weight assigned to period i of the growing season and r it is the effective rainfall in period i for year t. The weights w i can be chosen to maximize the sample correlation between the rainfall index and yields using data on rainfall and yield. 20

4 Payout procedure: The rainfall derivative for crops is structured to pay out when rainfall (R t ) in the crop year is below a specified threshold (T). The payment is proportional. The value of Rt is calculated by summing the value obtained multiplying rainfall in each period I of year t by specific weights assigned to every period I (equation 2) The indemnity is triggered according to the following function Indemnity = 0 if R t T T - R t if R t < T T Χ Liability Conclusion: With agriculture contributing to major portion of GDP in India and weather elements having prevalent and causal relationship with the production variables, weather derivatives can be effectively used to manage agricultural production risk. From the experience of the other developed countries, it can also be observed that weather derivatives can be useful means for addressing the systemic portion of agricultural risk, leading to potential applications in the stand-alone or layer structures in the re-insurance of agricultural risk exposure. Weather derivatives giving hedge against the agricultural risk happen to be cheaper and more effective than insurance schemes for agriculture. In order to support new developments in weather markets, at production or re-insurance levels, the regulators may also focus on providing infrastructure- in particular weather stations and free availability of weather data and supporting transaction costs for Weather Derivatives development. Reference: 1. Andrea Stoppa & Ulrich Hess: Design & Use of Weather Derivatives in Agricultural Policies. 2. Stephen Jewson & Rodrigo Caballero: The use of weather forecasts in the pricing of weather derivatives. 3. Robert Henderson: Pricing Weather Risk. 4. Mark Davis: Pricing weather derivatives by marginal value. 21

5 About the Authors: Anshul Anand Education: B.Com (h), Diploma in business finance, diploma in tax law. Currently pursuing Post Graduate Diploma in Actuarial Science. Surendra Mahadik Education: B.Sc.(Stats).,Paper passed CT1 from ASI Currently pursuing Post Graduate Diploma in Actuarial Science. 22

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