Real options valuation in energy markets
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Real options have been widely applied to analyze investment planning and asset valuation under uncertainty in many industries, especially energy markets. Because of their close analogy to financial options, real options can be valued using the classical financial option pricing theories and their extensions. However, as real options valuation often involves complex payoff structures and operational constraints of the underlying real assets or projects, accurate and flexible methods for solving the valuation problem are essential. This thesis investigates three different approaches to real options valuation and contributes to aspects of modeling realism and computational efficiency. The contributions are illustrated through two important applications of real options in energy markets: natural gas storage and power plant valuation. Because spread options are commonly used in basic real options valuation techniques, the first part of the thesis addresses the problems of spread option pricing and hedging. We develop a new closed-form approximation method for pricing two-asset spread options. Numerical analysis shows that our method is more accurate than existing analytical approximations. Our method is also extremely fast, with computing time more than two orders of magnitude shorter than one-dimensional numerical integration. Closed-form approximations for the Greeks of spread options are also developed. In addition, we analyze the price sensitivities of spread options and provide lower and upper bounds for digital spread options. We then further generalize the above results to multi-asset spread options on an arbitrary number of assets. We provide two new closed-form approximation methods for pricing spread options on a basket of risky assets: the extended Kirk approximation and the second-order boundary approximation. Numerical analysis shows that both methods are extremely fast and accurate, with the latter method more accurate than the former. Closed-form approximations for important Greeks are also derived. Because our approximation methods enable the accurate pricing of a bulk volume of spread options on two or more assets in real time, it offers traders a potential edge in a dynamic market environment. In the third part of this thesis, we propose a market-based valuation framework for valuing natural gas storage facility with realistic operational characteristics. The operational process is modeled as a multi-stage stochastic optimization problem. We develop a Gaussian quadrature scheme to solve for the dynamically optimal spot trading strategy and show that the computational efficiency of this method exceeds existing approaches in about two orders of magnitude. Furthermore, with this flexible quadrature scheme, we propose to value a gas storage based on a novel hybrid trading strategy that successfully incorporates both spot and forward trading, thus improving the storage valuation significantly by accounting for both the inter-month and intra-month operational flexibilities and price volatility. In the fourth part of this work, we develop a continuous-time formulation for power plant valuation in infinite time horizon. We propose a real-option-based model for a power plant to account for the embedded operational flexibility. This model incorporates start-up and shut-down costs as two major operational constraints. Under this continuous valuation model, spark spread is modeled directly as a continuous stochastic process to take account of the long term co-integration relationship between electricity and fuel prices. Instead of discretizing the stochastic process, we preserve continuity of the stochastic spark spread process and work directly with the value function. Closed-form of value function under threshold policy is obtained. The corresponding optimal operational strategy can then be solved. The advantage of this approach is that it reduces computational complexity while incorporates major operation characteristics. It enables fast computation of a power plant value that approximates the real market value and sensitivity analysis of the asset value with respect to the cost parameters of a power plant and the distribution parameters of spark spread.