Pricing Rainfall Derivatives Based on a Hidden Markov Model to Mitigate Poor Yield
Keywords:
Keywords: Hidden Markov model, Incomplete market, utility indifference, Hedging, Crop insurance, Weather derivatives, ARIMAAbstract
rainfall. The amount of monthly rainfall on wet days is obtained using auto-regressive moving average (ARIMA) models because the model is linear, since the future values are constrained to be linear functions of past data. Monthly rainfall data from 1995 to 2015 were taken from the Kamuzu International Airport (KIA) Meteorology station in order to assess the model performance. The selected model corresponds to the ARIMA (1,0,1) (2,0,1)12, and was validated by another historical rainfall data under the same conditions. The results obtained prove that the model could be used to model and forecast the future rainfall variability in Malawi. The steady state matrix from hidden Markov model (HMM) shows likelihood that rainfall pattern at Kamuzu International Airport (KIA) would follow the pattern of the given probabilities (0.396 0.604) which implies that the probability that it would rain on a particular day in future at KIA is 0.369 and the probability that it would be dry on a particular day is 0.604. As such, the study suggests the rainfall weather derivative as a solution to mitigate poor yield due to erratic rainfall. Therefore, the study suggests buying basket options. The utility indifference approach is used to derive the buyer’s and seller’s prices. Reasonably, the indifference approach starts with an interesting idea that the amount of money at which a possible buyer of a claim is indifferent in terms of expected utility between buying and selling creates an upper or lower limit for the contract price.
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