Pricing swing options and other electricity derivatives

The deregulation of regional electricity markets has led to more competitive prices but also higher uncertainty in the future electricity price development. Most markets exhibit high volatilities and occasional distinctive price spikes, which results in demand for derivative products which protect the holder against high prices. A good understanding of the stochastic price dynamics is required for the purposes of risk management and pricing derivatives. In this thesis we examine a simple spot price model which is the exponential of the sum of an Ornstein-Uhlenbeck and an independent pure jump process. We derive the moment generating function as well as various approximations to the probability density function of the logarithm of this spot price process at maturity T. With some restrictions on the set of possible martingale measures we show that the risk neutral dynamics remains within the class of considered models and hence we are able to calibrate the model to the observed forward curve and present semi-analytic formulas for premia of path-independent options as well as approximations to call and put options on forward contracts with and without a delivery period. In order to price path-dependent options with multiple exercise rights like swing contracts a grid method is utilised which in turn uses approximations to the conditional density of the spot process. Further contributions of this thesis include a short discussion of interpolation methods to generate a continuous forward curve based on the forward contracts with delivery periods observed in the market, and an investigation into optimal martingale measures in incomplete markets. In particular we present known results of q-optimal martingale measures in the setting of a stochastic volatility model and give a first indication of how to determine the q-optimal measure for q=0 in an exponential Ornstein-Uhlenbeck model consistent with a given forward curve

Commodity Derivatives Valuation with Autoregression and Moving Average in the Price Dynamics

In this paper we develop a continuous time factor model of commodity prices that allows for higher order autoregression and moving average components. The need for these components is documented by analyzing the convenience yield's time series dynamics. Making use of the affine model structure, closed-form pricing formulas for futures and options are derived. Empirically, a parsimonious version of the general model is estimated for the crude oil market using futures data. We demonstrate the model's superior performance in pricing nearby futures contracts in- and out-of-sample. Most notably, the model improves the pricing of long horizon contracts with information from the short end of the futures curve substantially.Commodity Pricing, CARMA, Futures, Crude Oil

Options on shipbuilding contracts

Thesis (S.B. and S.M.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1998.Includes bibliographical references (p. 123-124).Analysis of investment projects and strategic decisions using option theory has gained wide acceptance among corporate finance scholars and professionals. In the shipping and shipbuilding industries, option analysis is still in its infancy, and few professionals are familiar with option valuation tools. At the same time, practically all shipbuilding contracts contain option elements, the value of which most industry players do not know how to calculate. Newbuilding options give shipowners closing newbuilding contracts a right, but not an obligation, to enter into additional newbuilding contracts, with predetermined terms, at a later date. This thesis presents a general introduction to option theory as it applies to traded financial securities. This framework is extended to newbuilding options. Characteristics of the newbuilding markets are given, and fundamental stochastic processes that can describe newbuilding prices are introduced. Based on these stochastic processes, closed-form formulas for calculating the value of newbuilding options are presented. Actual observations of shipbuilding prices are analyzed in the context of the stochastic models. The results of this analysis are discussed as they apply to the option formulas and to the practical aspects of the newbuilding option framework. Recommendations are given on how to analyze real cases in which newbuilding options appear.by Morten W. Høegh.S.B.and S.M

Statistical analysis and stochastic interest rate modeling for valuing the future with implications in climate change mitigation

High future discounting rates favor inaction on present expend- ing while lower rates advise for a more immediate political action. A possible approach to this key issue in global economy is to take historical time series for nominal interest rates and inflation, and to construct then real interest rates and finally obtaining the resulting discount rate according to a specific stochastic model. Extended periods of negative real interest rates, in which inflation dominates over nominal rates, are commonly observed, occurring in many epochs and in all countries. This feature leads us to choose a well-known model in statistical physics, the Ornstein-Uhlenbeck model, as a basic dynamical tool in which real interest rates randomly fluctuate and can become negative, even if they tend to revert to a positive mean value. By covering 14 countries over hundreds of years we suggest different scenarios and include an error analysis in order to consider the impact of statistical uncertainty in our results. We find that only 4 of the countries have positive long-run discount rates while the other ten coun- tries have negative rates. Even if one rejects the countries where hyperinflation has occurred, our results support the need to consider low discounting rates. The results provided by these fourteen countries significantly increase the prior- ity of confronting global actions such as climate change mitigation. We finally extend the analysis by first allowing for fluctuations of the mean level in the Ornstein-Uhlenbeck model and secondly by considering modified versions of the Feller and lognormal models. In both cases, results remain basically unchanged thus demonstrating the robustness of the results presented

Asset Pricing under uncertainty

We study the effect of parameter uncertainty on a stochastic diffusion model, in particular the impact on the pricing of contingent claims, using methods from the theory of Dirichlet forms. We apply these techniques to hedging procedures in order to compute the sensitivity of SDE trajectories with respect to parameter perturbations. We show that this analysis can justify endogenously the presence of a bid-ask spread on the option prices. We also prove that if the stochastic differential equation admits a closed form representation then the sensitivities have closed form representations. We examine the case of log-normal diffusion and we show that this framework leads to a smiled implied volatility surface coherent with historical data.Comment: arXiv admin note: substantial text overlap with arXiv:1001.520

Climate derivatives: sharing the long-term climate related risks

Dopo aver compreso come il cambiamento climatico non colpisca tutti i settori economici alla stessa maniera e come gli strumenti finanziari già esistenti non siano in grado di soddisfare il bisogno di hedging dei rischi climatici, una possible soluzione è stata individuata nei climate derivatives. Un mercato per questi strumenti finanziari innovativi ancora non esiste in quanto sono stati solo progettati a livello teorico. Una volta esaminata la letteratura dei climate derivatives evidenziando punti di forza e di debolezza di ogni prototipo presentato, un metodo alternativo per il pricing di un tipo di derivato climatico, ovvero la temperature option, è proposto e testato attraverso simulazioni su Matlab.After having realized that climate change does not affect all economic sectors in the same way and that financial instruments already existing are not able to fulfill the need of hedging climate risks, a possible solution has been found in climate derivatives. A market for these novel financial instruments still does not exist: they have been only theoretically conceived. Once explored the literature of climate derivatives and highlighted strengths and weaknesses of each prototype presented, an alternative pricing method for a type of climate derivative, namely temperature option, is proposed and tested through Matlab simulations

A Comparative Analysis of 30 Bonus-Malus Systems

The automobile third party insurance merit-rating systems of 22 countries are simulated and compared, using as main tools the stationary average premium level, the variability of the policyholders\u27 payments, their elasticity with respect to the claim frequency, and the magnitude of the hunger for bonus. Principal components analysis is used to define an “Index of Toughness” for all systems

Real options for adaptive decisions in primary industries

Abstract The long term sustainability of Australian crop and livestock farms is threatened with climate change and climate variability. In response, farmers may decide to (1) adjust practices and technologies, (2) change production systems, or (3) transform their industries, for example, by relocating to new geographical areas. Adjustments to existing practices are easy to make relative to changes to production systems or transformations of an industry. Switching between production regimes requires new investments and infrastructure and can leave assets stranded. These changes can be partially or wholly irreversible but hysteresis effects can make switching difficult and mistakes costly to reverse. ‘Real options’ is a framework to structure thinking and analysis of these difficult choices. Previous work has demonstrated how real options can be applied to adaptation, and extends traditional economic analyses of agricultural investment decisions based on net present values to better represent the uncertainty and risks of climate change. This project uses transects across space as analogues for future climate scenarios. We simulate yields from climate data and draw on data from actual farms to estimate a real options model referred to as ‘Real Options for Adaptive Decisions’ (ROADs). We present results for the transformation of wheat dominant cropping systems in South Australia, New South Wales, and Western Australia. We find that farmers’ decisions, as much as a changing climate, determine how agriculture will be transformed. Please cite this report as: Hertzler, G, Sanderson, T, Capon, T, Hayman, P, Kingwell, R, McClintock, A, Crean, J, Randall, A 2013 Will primary producers continue to adjust practices and technologies, change production systems or transform their industry – an application of real options,  National Climate Change Adaptation Research Facility, Gold Coast, pp. 93. The long term sustainability of Australian crop and livestock farms is threatened with climate change and climate variability. In response, farmers may decide to (1) adjust practices and technologies, (2) change production systems, or (3) transform their industries, for example, by relocating to new geographical areas. Adjustments to existing practices are easy to make relative to changes to production systems or transformations of an industry. Switching between production regimes requires new investments and infrastructure and can leave assets stranded. These changes can be partially or wholly irreversible but hysteresis effects can make switching difficult and mistakes costly to reverse. ‘Real options’ is a framework to structure thinking and analysis of these difficult choices. Previous work has demonstrated how real options can be applied to adaptation, and extends traditional economic analyses of agricultural investment decisions based on net present values to better represent the uncertainty and risks of climate change. This project uses transects across space as analogues for future climate scenarios. We simulate yields from climate data and draw on data from actual farms to estimate a real options model referred to as ‘Real Options for Adaptive Decisions’ (ROADs). We present results for the transformation of wheat dominant cropping systems in South Australia, New South Wales, and Western Australia. We find that farmers’ decisions, as much as a changing climate, determine how agriculture will be transformed

Review of stochastic differential equations in statistical arbitrage pairs trading

The use of stochastic differential equations offers great advantages for statistical arbitrage pairs trading. In particular, it allows the selection of pairs with desirable properties, e.g., strong mean-reversion, and it renders traditional rules of thumb for trading unnecessary. This study provides an exhaustive survey dedicated to this field by systematically classifying the large body of literature and revealing potential gaps in research. From a total of more than 80 relevant references, five main strands of stochastic spread models are identified, covering the ‘Ornstein–Uhlenbeck model’, ‘extended Ornstein–Uhlenbeck models’, ‘advanced mean-reverting diffusion models’, ‘diffusion models with a non-stationary component’, and ‘other models’. Along these five main categories of stochastic models, we shed light on the underlying mathematics, hereby revealing advantages and limitations for pairs trading. Based on this, the works of each category are further surveyed along the employed statistical arbitrage frameworks, i.e., analytic and dynamic programming approaches. Finally, the main findings are summarized and promising directions for future research are indicated