Modeling and Forecasting CAT and HDD Indices For Weather Derivative Pricing

In this paper, we use wavelet neural networks in order to model a mean-reverting Ornstein–Uhlenbeck temperature process, with seasonality in the level and volatility and time-varying speed of mean reversion. We forecast up to 2 months ahead out of sample daily temperatures, and we simulate the corresponding Cumulative Average Temperature and Heating Degree Day indices. The proposed model is validated in 8 European and 5 USA cities all traded in the Chicago Mercantile Exchange. Our results suggest that the proposed method outperforms alternative pricing methods, proposed in prior studies, in most cases. We find that wavelet networks can model the temperature process very well and consequently they constitute an accurate and efficient tool for weather derivatives pricing. Finally, we provide the pricing equations for temperature futures on Cooling and Heating Degree Day indices

Pricing of Asian temperature risk

Weather derivatives (WD) are different from most financial derivatives because the underlying weather cannot be traded and therefore cannot be replicated by other financial instruments. The market price of risk (MPR) is an important parameter of the associated equivalent martingale measures used to price and hedge weather futures/options in the market. The majority of papers so far have priced non-tradable assets assuming zero MPR, but this assumption underestimates WD prices. We study the MPR structure as a time dependent object with concentration on emerging markets in Asia. We find that Asian Temperatures (Tokyo, Osaka, Beijing, Teipei) are normal in the sense that the driving stochastics are close to a Wiener Process. The regression residuals of the temperature show a clear seasonal variation and the volatility term structure of CAT temperature futures presents a modified Samuelson effect. In order to achieve normality in standardized residuals, the seasonal variation is calibrated with a combination of a fourier truncated series with a GARCH model and with a local linear regression. By calibrating model prices, we implied the MPR from Cumulative total of 24- hour average temperature futures (C24AT) for Japanese Cities, or by knowing the formal dependence of MPR on seasonal variation, we price derivatives for Kaohsiung, where weather derivative market does not exist. The findings support theoretical results of reverse relation between MPR and seasonal variation of temperature process.Weather derivatives, continuous autoregressive model, CAT, CDD, HDD, risk premium

Is temperature-index derivative suitable for China?

In this paper, we assessed the suitability of temperature derivatives for China through modeling. We assumed that if the physical dynamics of temperature of some cities are identical, then the same types of temperature derivatives can be used in these cities. Nearly twenty years temperature data of forty-seven cities with traded temperature derivatives on the Chicago Mercantile Exchange Group (CME) and seven Chinese cities were collected and analyzed in a two-step approach. Firstly, the AR-EGARCH model capturing the shock asymmetry of the volatility of temperature is used to simulate the dynamics of temperature of the cities. Secondly, the temperature of the cities are classified through cluster analysis based on model parameters from the AR-EGARCH model. The results showed that the fitting effect of the AR-EGARCH model is very good, and only a few cities did not display the shock asymmetry. The model for Nanjing fitted well into one of the categories of the cities in the CME; but the other six Chinese cities belong to new categories, which are different from the cities in the CME. We concluded that HDD and CAT in Europe and CAT∗ in Japan can be used directly in Nanjing, but the existing temperature derivatives in CME were unsuitable for the other six Chinese cities. Recommendations for the establishment of weather derivatives market in China have been proposed

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

A consistent two-factor model for pricing temperature derivatives

We analyze a consistent two-factor model for pricing temperature derivatives that incorporates the forward looking information available in the market by specifying a model for the dynamics of the complete meteorological forecast curve. The two-factor model is a generalization of the Nelson-Siegel curve model by allowing factors with mean-reversion to a stochastic mean for structural changes and seasonality for periodic patterns. Based on the outcomes of a statistical analysis of forecast data we conclude that the two-factor model captures well the stylized features of temperature forecast curves. In particular, a functional principal component analysis reveals that the model re ects reasonably well the dynamical structure of forecast curves by decomposing their shapes into a tilting and a bending factor. We continue by developing an estimation procedure for the model, before we derive explicit prices for temperature derivatives and calibrate the market price of risk (MPR) from temperature futures derivatives (CAT, HDD, CDD) traded at the Chicago Mercantile Exchange (CME). The factor model shows that the behavior of the implied MPR for futures traded in and out of the measurement period is more stable than other estimates obtained in the literature. This confirms that at least parts of the irregularity of the MPR is not due to irregular risk perception but rather due to information misspecification. Similar to temperature derivatives, this approach can be used for pricing other non-tradable assets

Model based Monte Carlo pricing of energy and temperature quanto options

Weather derivatives have become very popular tools in weather risk management in recent years. One of the elements supporting their diffusion has been the increase in volatility observed on many energy markets. Among the several available contracts, Quanto options are now becoming very popular for a simple reason: they take into account the strong correlation between energy consumption and certain weather conditions, so enabling price and weather risk to be controlled at the same time. These products are more efficient and, in many cases, significantly cheaper than simpler plain vanilla options. Unfortunately, the specific features of energy and weather time series do not enable the use of analytical formulae based on the Black-Scholes pricing approach, nor other more advanced continuous time methods that extend the Black-Scholes approach, unless under strong and unrealistic assumptions. In this study, we propose a Monte Carlo pricing framework based on a bivariate time series model. Our approach takes into account the average and variance interdependence between temperature and energy price series. Furthermore, our approach includes other relevant empirical features, such as periodic patterns in average, variance, and correlations. The model structure enables a more appropriate pricing of Quanto options compared to traditional methods.weather derivatives; Quanto options pricing; derivative pricing; model simulation; forecast

Robust portfolio selection problem under temperature uncertainty

In this paper, we consider a portfolio selection problem under temperature uncertainty. Weather derivatives based on different temperature indices are used to protect against undesirable temperature events. We introduce stochastic and robust portfolio optimization models using weather derivatives. The investors’ different risk preferences are incorporated into the portfolio allocation problem. The robust investment decisions are derived in view of discrete and continuous sets that the underlying uncertain data in temperature model belong. We illustrate main features of the robust approach and performance of the portfolio optimization models using real market data. In particular, we analyze impact of various model parameters on different robust investment decisions

Some applications of higher-order hidden Markov models in the exotic commodity markets

The liberalisation of regional and global commodity markets over the last several decades resulted in certain commodity price behaviours that require new modelling and estimation approaches. Such new approaches have important implications to the valuation and utilisation of commodity derivatives. Derivatives are becoming increasingly crucial for market participants in hedging their exposure to volatile price swings and in managing risks associated with derivative trading. The modelling of commodity-based variables is an integral part of risk management and optimal-investment strategies for commodity-linked portfolios. The characteristics of commodity price evolution cannot be captured sufficiently by one-state driven models even with the inclusion of multiple factors. This inspires the adoption of regime-switching methods to rectify the one-state multi-factor modelling inadequacies. In this research, we aim to employ higher-order hidden Markov models (HOHMMs) in order to take advantage of the latent information in the observed process recorded in the past. This hugely enhances and complements the regime-switching features of our approach in describing certain variables that virtually determine the value of some commodity derivatives such as contracts dependent on temperature, electricity spot price, and fish-price dynamics. Our push for the utility of the change-of-probability-measure technique facilitates the derivation of recursive filtering algorithms. This then establishes a self-tuning dynamic estimation procedure. Both the data-fitting and forecasting performances of various model settings are investigated. This research work emerged from four related projects detailed as follows. (i) We start with an HMM to model the behaviour of daily average temperatures (DATs) geared towards the analysis of weather derivatives. (ii) The model in (i) is extended naturally by showcasing the capacity of an HOHMM-based approach to simultaneously describe the DATs’ salient properties of mean reversion, seasonality, memory and stochasticity. (iii) An HOHMM-driven jump process augments the HOHMM-based de-seasonalised temperature process to capture price spikes, and the ensuing filtering algorithms under this modelling framework are constructed to provide optimal parameter estimates. (iv) Finally, a multi-dimensional HOHMM-modulated set up is built for futures price-curve dynamics pertinent to financial product valuation and risk management in the aquaculture sector. We examine the performance of this new modelling set up by considering goodness-of-fit and out-of-sample forecasting metrics with a detailed numerical demonstration using a multivariate dataset compiled by the Fish Pool ASA. This research offers a collection of more flexible stochastic modelling approaches for pricing and risk analysis of certain commodity derivatives on weather, electricity and fish prices. The novelty of our techniques is the powerful capability to automate the parameter estimation. Consequently, we contribute to the development of financial tools that aid in selecting the appropriate and optimal model on the basis of some information criteria and within current technological advancements in which continuous flow of observed data are now readily accessible in real time