Pricing Rainfall Based Futures Using Genetic Programming

Rainfall derivatives are in their infancy since starting trading on the Chicago Mercantile Exchange (CME) since 2011. Being a relatively new class of financial instruments there is no generally recognised pricing framework used within the literature. In this paper, we propose a novel framework for pricing contracts using Genetic Programming (GP). Our novel framework requires generating a risk-neutral density of our rainfall predictions generated by GP supported by Markov chain Monte Carlo and Esscher transform. Moreover, instead of having a single rainfall model for all contracts, we propose having a separate rainfall model for each contract. We compare our novel framework with and without our proposed contract-specific models for pricing against the pricing performance of the two most commonly used methods, namely Markov chain extended with rainfall prediction (MCRP), and burn analysis (BA) across contracts available on the CME. Our goal is twofold, (i) to show that by improving the predictive accuracy of the rainfall process, the accuracy of pricing also increases. (ii) contract-specific models can further improve the pricing accuracy. Results show that both of the above goals are met, as GP is capable of pricing rainfall futures contracts closer to the CME than MCRP and BA. This shows that our novel framework for using GP is successful, which is a significant step forward in pricing rainfall derivatives

Stochastic model genetic programming: Deriving pricing equations for rainfall weather derivatives

Rainfall derivatives are in their infancy since starting trading on the Chicago Mercantile Exchange (CME) in 2011. Being a relatively new class of financial instruments there is no generally recognised pricing framework used within the literature. In this paper, we propose a novel Genetic Programming (GP) algorithm for pricing contracts. Our novel algorithm, which is called Stochastic Model GP (SMGP), is able to generate and evolve stochastic equations of rainfall, which allows us to probabilistically transform rainfall predictions from the risky world to the risk-neutral world. In order to achieve this, SMGP's representation allows its individuals to comprise of two weighted parts, namely a seasonal component and an autoregressive component. To create the stochastic nature of an equation for each SMGP individual, we estimate the weights by using a probabilistic approach. We evaluate the models produced by SMGP in terms of rainfall predictive accuracy and in terms of pricing performance on 42 cities from Europe and the USA. We compare SMGP to 8 methods: its predecessor DGP, 5 well-known machine learning methods (M5 Rules, M5 Model trees, k-Nearest Neighbors, Support Vector Regression, Radial Basis Function), and two statistical methods, namely AutoRegressive Integrated Moving Average (ARIMA) and Monte Carlo Rainfall Prediction (MCRP). Results show that the proposed algorithm is able to statistically outperform all other algorithms

Feature Engineering for Improving Financial Derivatives-based Rainfall Prediction

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 extending previous work carried out on the prediction of rainfall using Genetic Programming (GP) for rainfall derivatives. Currently in the rainfall derivatives literature, the process of predicting rainfall is dominated by statistical models, namely using a Markov-chain extended with rainfall prediction (MCRP). In this paper we further extend our new methodology by looking at the effect of feature engineering on the rainfall prediction process. Feature engineering will allow us to extract additional information from the data variables created. By incorporating feature engineering techniques we look to further tailor our GP to the problem domain and we compare the performance of the previous GP, which previously statistically outperformed MCRP, against our new GP using feature engineering on 21 different data sets of cities across Europe and report the results. The goal is to see whether GP can outperform its predecessor without extra features, which acts as a benchmark. Results indicate that in general GP using extra features significantly outperforms a GP without the use of extra features

New Genetic Programming Methods for Rainfall Prediction and Rainfall Derivatives Pricing

Rainfall derivatives is a part of an umbrella concept of weather derivatives, whereby the underlying weather variable determines the value of derivative, in our case the rainfall. These financial contracts are currently in their infancy as they have started trading on the Chicago Mercantile Exchange (CME) since 2011. Such contracts are very useful for investors or trading firms who wish to hedge against the direct or indirect adverse effects of the rainfall. The first crucial problem to focus on in this thesis is the prediction of the level of rainfall. In order to predict this, two techniques are routinely used. The first most commonly used approach is Markov chain extended with rainfall prediction. The second approach is Poisson-cluster model. Both techniques have some weakness in their predictive powers for rainfall data. More specifically, a large number of rainfall pathways obtained from these techniques are not representative of future rainfall levels. Additionally, the predictions are heavily influenced by the prior information, leading to future rainfall levels being the average of previously observed values. This motivates us to develop a new algorithm to the problem domain, based on Genetic Programming (GP), to improve the prediction of the underlying variable rainfall. GP is capable of producing white box (interpretable, as opposed to black box) models, which allows us to probe the models produced. Moreover, we can capture nonlinear and unexpected patterns in the data without making any strict assumptions regarding the data. The daily rainfall data represents some difficulties for GP. The difficulties include the data value being non-negative and discontinuous on the real time line. Moreover, the rainfall data consists of high volatilities and low seasonal time series. This makes the rainfall derivatives much more challenging to deal with than other weather contracts such as temperature or wind. However, GP does not perform well when it is applied directly on the daily rainfall data. We thus propose a data transformation method that improves GP's predictive power. The transformation works by accumulating the daily rainfall amounts into accumulated amounts with a sliding window. To evaluate the performance, we compare the prediction accuracy obtained by GP against the most currently used approach in rainfall derivatives, and six other machine learning algorithms. They are compared on 42 different data sets collected from different cities across the USA and Europe. We discover that GP is able to predict rainfall more accurately than the most currently used approaches in the literature and comparably to other machine learning methods. However, we find that the equations generated by GP are not able to take into account the volatilities and extreme periods of wet and dry rainfall. Thus, we propose decomposing the problem of rainfall into 'sub problems' for GP to solve. We decompose the time series of rainfall by creating a partition to represent a selected range of the total rainfall amounts, where each partition is modelled by a separate equation from GP. We use a Genetic Algorithm to assist with the partitioning of data. We find that through the decomposition of the data, we are able to predict the underlying data better than all machine learning benchmark methods. Moreover, GP is able to provide a better representation of the extreme periods in the rainfall time series. The natural progression is to price rainfall futures contracts from rainfall prediction. Unlike other pricing domains in the trading market, there is no generally recognised pricing framework used within the literature. Much of this is due to weather derivatives (including rainfall derivatives) existing in an incomplete market, where the existing and well-studied pricing methods cannot be directly applied. There are two well-known techniques for pricing, the first is through indifference pricing and the second is through arbitrage free pricing. One of the requirements for pricing is knowing the level of risk or uncertainty that exists within the market. This allows for a contract price free of arbitrage. GP can be used to price derivatives, but the risk cannot be directly estimated. To estimate the risk, we must calculate a density of proposed rainfall values from a single GP equation, in order to calculate the most probable outcome. We propose three methods to achieve the required results. The first is through the procedure of sampling many different equations and extrapolating a density from the best of each generation over multiple runs. The second proposal builds on the first considering contract-specific equations, rather than a single equation explaining all contracts before extrapolating a density. The third method is the proposition of GP evolving and creating a collection of stochastic equations for pricing rainfall derivatives. We find that GP is a suitable method for pricing and both proposed methods are able to produce good pricing results. Our first and second methods are capable of pricing closer to the rainfall futures prices given by the CME. Moreover, we find that our third method reproduces the actual rainfall for the specified period of interest more accurately

Scenario driven optimal sequencing under deep uncertainty

Abstract not availableEva H.Y. Beh, Holger R. Maier, Graeme C. Dand

A Comparison between Wavelet Networks and Genetic Programming in the Context of Temperature Derivatives

The purpose of this study is to develop a model that accurately describes the dynamics of the daily average temperature in the context of weather derivatives pricing. More precisely we compare two state of the art machine learning algorithms, namely wavelet networks and genetic programming, against the classic linear approaches widely used in the pricing of temperature derivatives in the financial weather market and against various machine learning benchmark models such as neural networks, radial basis functions and support vector regression. The accuracy of the valuation process depends on the accuracy of the temperature forecasts. Our proposed models are evaluated and compared in-sample and out-of-sample in various locations where weather derivatives are traded. Furthermore, we expand our analysis by examining the stability of the forecasting models relative to the forecasting horizon. Our findings suggest that the proposed nonlinear methods significantly outperform the alternative linear models, with wavelet networks ranking first, and can be used for accurate weather derivative pricing in the weather market

Responsiveness of Demand for Irrigation Water: A Focus on the Southern Murray-Darling Basin

The Productivity Commission staff working paper, 'Responsiveness of Demand for Irrigation Water: A Focus on the Southern Murray-Darling Basin', was released August 2004. This paper explores the determinants of the elasticity of demand for irrigation water. It focuses on three main irrigated industries - rice, dairy and horticulture - to gain a greater understanding of the value that farmers place on water as an input. This paper provides detail relating to farm decision behaviour and biophysical production realities faced by irrigators in the southern Murray-Darling Basin. The views expressed in this paper are those of the staff involved and do not necessarily reflect those of the Productivity Commission.Resource /Energy Economics and Policy,

Applications of Genetic Programming to Finance and Economics: Past, Present, Future

While the origins of Genetic Programming (GP) stretch back over fifty years, the field of GP was invigorated by John Koza’s popularisation of the methodology in the 1990s. A particular feature of the GP literature since then has been a strong interest in the application of GP to real-world problem domains. One application domain which has attracted significant attention is that of finance and economics, with several hundred papers from this subfield being listed in the Genetic Programming Bibliography. In this article we outline why finance and economics has been a popular application area for GP and briefly indicate the wide span of this work. However, despite this research effort there is relatively scant evidence of the usage of GP by the mainstream finance community in academia or industry. We speculate why this may be the case, describe what is needed to make this research more relevant from a finance perspective, and suggest some future directions for the application of GP in finance and economics

Managing Risk in Farming: Concepts, Research, and Analysis

The risks confronted by grain and cotton farmers are of particular interest, given the changing role of the Government after passage of the 1996 Farm Act. With the shift toward less government intervention in the post-1996 Farm Act environment, a more sophisticated understanding of risk and risk management is important to help producers make better decisions in risky situations and to assist policymakers in assessing the effectiveness of different types of risk protection tools. In response, this report provides a rigorous, yet accessible, description of risk and risk management tools and strategies at the farm level. It also provides never-before-published data on farmers' assessments of the risks they face, their use of alternative risk management strategies, and the changes they would make if faced with financial difficulty. It also compares price risk across crops and time periods, and provides detailed information on yield variability.crop insurance, diversification, futures contracts, leasing, leveraging, liquidity, livestock insurance, marketing contracts, options contracts, production contracts, revenue insurance, risk, vertical integration, Farm Management, Risk and Uncertainty,