Predicting Rainfall in the Context of Rainfall Derivatives Using Genetic Programming

Abstract

Abstract-Rainfall is one of the most challenging variables to predict, as it exhibits very unique characteristics that do not exist in other time series data. Moreover, rainfall is a major component and is essential for applications that surround water resource planning. In particular, this paper is interested in the prediction of rainfall for rainfall derivatives. Currently in the rainfall derivatives literature, the process of predicting rainfall is dominated by statistical models, namely using a Markovchain extended with rainfall prediction (MCRP). In this paper we outline a new methodology to be carried out by predicting rainfall with Genetic Programming (GP). This is the first time in the literature that GP is used within the context of rainfall derivatives. We have created a new tailored GP to this problem domain and we compare the performance of the GP and MCRP on 21 different data sets of cities across Europe and report the results. The goal is to see whether GP can outperform MCRP, which acts as a benchmark. Results indicate that in general GP significantly outperforms MCRP, which is the dominant approach in the literature.

Pricing Rainfall Based Futures Using Genetic Programming

“…By developing this approach, we are able to price rainfall derivatives using the Esscher transform, a popular technique for calculating risk premiums. The motivation for this paper comes from the work of [9,8,7] where GP was used to predict the rainfall time series with a range of alternative approaches across European cities. However, the work did not present information on pricing.…”

“…For this paper we use the GP outlined in [7], which is a hybrid GP that decomposed the problem of rainfall prediction into smaller subproblems assisted by a Genetic Algorithm (GA). For details of this technique, hereafter referred to as GP/GA, see [9]. GP/GA has been shown to outperform the current approach of MCRP on European data sets.…”

“…To maximise the predictive performance of GP before pricing, we use the data transformation proposed in [9] to smooth the problem landscape. As an example, Figure 1a shows the original daily rainfall data for Detroit, and Figure 1b shows the result of the data transformation.…”

“…In order to predict the level of rainfall for rainfall derivatives, Markov-chain extended with rainfall prediction (MCRP) [19] and spatial-temporal rainfall (STR) models [18] have been used. More recently, Genetic Programming (GP) has been applied as an alternative predictive technique [9,8,7]. By predicting the underlying variable of rainfall, this increases the accuracy of pricing, which is crucial because contracts are priced ahead of time-up to a year ahead.…”

“…We use GP for three reasons, (i) GP has been shown to outperform the standard approach of MCRP in [9,8,7]. (ii) There is a correlation between predictive accuracy and pricing accuracy [12,1], meaning that GP should improve pricing performance.…”