Antonis Alexandridis

Modelling the Temperature Time-dependent Speed of Mean Reversion in the Context of Weather Derivatives Pricing

In this paper, in the context of an Ornstein–Uhlenbeck temperature process, we use neural networks to examine the time dependence of the speed of the mean reversion parameter α of the process. We estimate non‐parametrically with a neural network a model of the temperature process and then compute the derivative of the network output w.r.t. the network input, in order to obtain a series of daily values for α. To our knowledge, this is the first time that this has been done, and it gives us a much better insight into the temperature dynamics and temperature derivative pricing. Our results indicate strong time dependence in the daily values of α, and no seasonal patterns. This is important, since in all relevant studies performed thus far, α was assumed to be constant. Furthermore, the residuals of the neural network provide a better fit to the normal distribution when compared with the residuals of the classic linear models used in the context of temperature modelling (where α is constant). It follows that by setting the mean reversion parameter to be a function of time we improve the accuracy of the pricing of the temperature derivatives. Finally, we provide the pricing equations for temperature futures, when α is time dependent.

Weather derivatives pricing: Modeling the seasonal residual variance of an Ornstein-Uhlenbeck temperature process with neural networks

In this paper, we use neural networks in order to model the seasonal component of the residual variance of a mean-reverting Ornstein-Uhlenbeck temperature process, with seasonality in the level and volatility. This approach can be easily used for pricing weather derivatives by performing Monte Carlo simulations. Moreover, in synergy with neural networks we use wavelet analysis to identify the seasonality component in the temperature process as well as in the volatility of the temperature anomalies. Our model is validated on more than 100 years of data collected from Paris, one of the European cities traded at Chicago Mercantile Exchange. Our results show a significant improvement over more traditional alternatives, regarding the statistical properties of the temperature process. This is important since small misspecifications in the temperature process can lead to large pricing errors.

Introduction to Stochastic Calculus

The purpose of this chapter is to give the necessary background in stochastic calculus. It is not meant to provide a complete background in stochastic theory but rather present all the necessary theorems and results that will be used later on in order to derive the prices of various weather derivatives on different weather indexes. The reader, familiar or not to stochastic calculus, may use this chapter as a reference.

Predicting Rainfall in the Context of Rainfall Derivatives Using Genetic Programming

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 Markov-chain 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.

An extensive evaluation of seven machine learning methods for rainfall prediction in weather derivatives

Regression problems provide some of the most challenging research opportunities in the area of machine learning, and more broadly intelligent systems, where the predictions of some target variables are critical to a specific application. Rainfall is a prime example, as it exhibits unique characteristics of high volatility and chaotic patterns that do not exist in other time series data. This work’s main impact is to show the benefit machine learning algorithms, and more broadly intelligent systems have over the current state-of-the-art techniques for rainfall prediction within rainfall derivatives. We apply and compare the predictive performance of the current state-of-the-art (Markov chain extended with rainfall prediction) and six other popular machine learning algorithms, namely: Genetic Programming, Support Vector Regression, Radial Basis Neural Networks, M5 Rules, M5 Model trees, and k-Nearest Neighbours. To assist in the extensive evaluation, we run tests using the rainfall time series across data sets for 42 cities, with very diverse climatic features. This thorough examination shows that the machine learning methods are able to outperform the current state-of-the-art. Another contribution of this work is to detect correlations between different climates and predictive accuracy. Thus, these results show the positive effect that machine learning-based intelligent systems have for predicting rainfall based on predictive accuracy and with minimal correlations existing across climates.

Model Identification in Wavelet Neural Networks Framework

The scope of this study is to present a complete statistical framework for model identification of wavelet neural networks (WN). In each step in WN construction we test various methods already proposed in literature. In the first part we compare four different methods for the initialization and construction of the WN. Next various information criteria as well as sampling techniques proposed in previous works were compared to derive an algorithm for selecting the correct topology of a WN. Finally, in variable significance testing the performance of various sensitivity and model-fitness criteria were examined and an algorithm for selecting the significant explanatory variables is presented.

Pricing Approaches of Temperature Derivatives

This chapter reviews in detail the most important and more often cited models proposed in literature to represent the temperature driving process. In this chapter, the strengths and weaknesses of prior studies will be analyzed in order to develop an appropriate model that describes the temperature dynamics and that it can be used in pricing of various temperature derivatives.

Pricing Rainfall Based Futures Using Genetic Programming

Rainfall derivatives are in their infancy since starting trading on the Chicago Mercentile 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.

Pricing the Power of Wind

Wind is considered to be a free, renewable, and environmentally friendly source of energy. However, wind farms are exposed to excessive weather risk since the power production depends on the wind speed and the wind direction. In this chapter, the dynamics of the wind-generating process are modeled using a nonparametric nonlinear wavelet network. Our model is validated in New York. Our results indicate that wavelet networks can model the wind process very well and consequently, and they constitute an accurate and efficient tool for wind derivatives pricing. Finally, we provide the pricing equations for wind futures written on two indices, the cumulative average wind speed index and the Nordix wind speed index.

The Effects of the Geographical and Basis Risk

This chapter reviews in detail the notion of basis risk in the weather market. In contrast to classical financial markets, basis risk in the sense of weather derivatives has a different definition. First, the notion of geographical basis risk is analyzed, and a spatial model for temperature is presented. Next, the basis risk between the revenues of a company from electricity sector that uses weather derivatives and a weather variable is discussed. The payoff of a weather derivative depends on a weather index and not on the actual amount of money lost due to weather; although temperature and electricity consumption are highly correlated, it is unlikely that the payoff will compensate exactly for the money lost.