Valuing portfolios of interdependent real options using influence diagrams and simulation-and-regression: A multi-stage stochastic integer programming approach

Although real options generally occur within portfolios, most valuation approaches based on either option pricing or decision analysis alone focus on single well-defined options. In this paper we present a new approach for modelling and approximating the value of portfolios of interdependent real options using both influence diagrams and simulation-and-regression. The key feature of this approach is that it translates the interdependencies between real options into a set of constraints and then directly models the dynamics of all underlying uncertainties using (Markovian) stochastic processes. These are then integrated in a portfolio optimisation problem which is formulated as a multi-stage stochastic integer program. Applying a simulation and parametric regression approach to approximate the value of this optimisation problem, we present a transparent valuation algorithm that explicitly takes into account vector-valued exercise decisions and the state variable’s multidimensional resource component. The approach is therefore applicable to a wide range of complex investment projects with both inherent interdependent flexibilities and many underlying uncertainties. The approach is illustrated by evaluating a complex natural resource investment that features both a large portfolio of interdependent real options and four stochastic factors. We analyse the way in which the approximated value of the portfolio and its individual options are affected by the initial copper price as well as by the degrees of production cost and copper price uncertainty

Monte Carlo Valuation of natural gas investments

This paper deals with the valuation of energy assets related to natural gas. In particular, we evaluate a baseload Natural Gas Combined Cycle (NGCC) power plant and an ancillary instalation, namely a Liquefied Natural Gas (LNG) facility, in a realistic setting; specifically, these investments enjoy a long useful life but require some non-negligible time to build. Then we focus on the valuation of several investment options again in a realistic setting. These include the option to invest in the power plant when there is uncertainty concerning the initial outlay, or the option's time to maturity, or the cost of CO2 emission permits, or when there is a chance to double the plant size in the future. Our model comprises three sources of risk. We consider uncertain gas prices with regard to both the current level and the long-run equilibrium level; the current electricity price is also uncertain. They all are assumed to show mean reversion. The two-factor model for natural gas price is calibrated using data from NYMEX NG futures contracts. Also, we calibrate the one-factor model for electricity price using data from the Spanish wholesale electricity market, respectively. Then we use the estimated parameter values alongside actual physical parameters from a case study to value natural gas plants. Finally, the calibrated parameters are also used in a Monte Carlo simulation framework to evaluate several American-type options to invest in these energy assets. We accomplish this by following the least squares MC approach.real options, power plants, stochastic revenues and cost, CO2 allowances, LNG

Valoraciones exóticas: El caso de opciones americanas con barreras estocásticas

En este documento proponemos una nueva metodología de valoración de opciones americanas con características exóticas mediante la valoración de un portafolio de opciones europeas con diverso vencimiento. Nuestros resultados muestran que: (i) la metodología es numéricamente robusta en la valoración de opciones americanas simples; (ii) las valoraciones del modelo corresponden a las ofertas y primas observadas en las subastas de un conjunto de opciones multidimensionales que integran elementos de opciones trinquete, asiáticas y barrera; y (iii) la forma cerrada de nuestra aproximación permite la derivación de una solución analítica para las griegas de la opción que caracterizan la exposición a diversos factores de riesgo. Finalmente, resaltamos que nuestro modelo requiere menos del 1% del tiempo de ejecución computacional comparado a otros métodos estándar como simulaciones de Monte Carlo.We develop a novel pricing strategy that approximates the value of an American option with exotic features through a portfolio of European options with different maturities. Among our findings, we show that: (i) our model is numerically robust in pricing plain vanilla American options; (ii) the model matches observed bids and premiums of multidimensional options that integrate Ratchet, Asian, and Barrier characteristics; and (iii) our closed-form approximation allows for an analytical solution of the option’s greeks, which characterize the sensitivity to various risk factors. Finally, we highlight that our estimation requires less than 1% of the computational time compared to other standard methods, such as Monte Carlo simulations.Valoraciones exóticas: El caso de opciones americanas con barreras estocásticas Objetivo Proponemos un método de valoración de opciones Americanas con componentes exóticos que permite superar algunos problemas numéricos que encontramos en la implementación de simulaciones de Monte Carlo en el contexto de opciones de volatilidad subastadas por el Banco de la República. Contribución Construimos una estrategia de valoración de opciones Americanas con características exóticas a la que denominamos ponderación del valor temporal. En esta metodología aproximamos el valor de una opción americana a través de un portafolio de opciones europeas, en donde su valor temporal sirve para calibrar los pesos del portafolio. Las opciones estudiadas conjugan elementos exóticos de opciones trinquete, asiáticas, barrera y multidimensional. Resaltamos que el tiempo de computación de nuestro método es inferior al del tiempo requerido por mínimos cuadrados de Monte Carlo, por lo cual, nuestra propuesta puede ser de utilidad para agentes del mercado financiero que requieran una estimación rápida y precisa sobre la prima de una opción. Resultados En primer lugar, la metodología de ponderación del valor temporal es estadísticamente robusta en la valoración de la prima de opciones Americanas con componentes exóticos. En comparación con mínimos cuadrados de Monte Carlo, las primas estimadas por nuestro modelo son más precisas y estables. En segundo lugar, en el caso de las opciones de volatilidad subastadas por el Banco de la República encontramos que el precio estimado es comparable a las ofertas y primas de las subastas realizadas. Adicionalmente, los intermediarios del mercado financiero que toman la posición larga en estas opciones están principalmente expuestos a la volatilidad de la tasa de cambio. FRASE DESTACADA Nuestra propuesta puede ser de utilidad para agentes del mercado financiero que requieran una estimación rápida y precisa sobre la prima de una opción

Valuing infrastructure investments as portfolios of interdependent real options

The value of infrastructure investments is frequently influenced by enormous uncertainty surrounding both exogenous and endogenous factors. At the same time, however, their value is generally driven by much flexibility - i.e. options - with respect to design, financing, construction and operation. Real options analysis aims to pro-actively manage risks by valuing the flexibilities inherent in uncertain investments. Although real options generally occur within portfolios whose value is affected by both exogenous and endogenous uncertainty, most existing valuation approaches focus on single (i.e. individual) options and consider only exogenous uncertainty. In this thesis, we introduce an approach for modelling and approximating the value of portfolios of interdependent real options under exogenous uncertainty, using both influence diagrams and simulation-and-regression. The key features of this approach are that it translates the interdependencies between real options into linear constraints and then integrates these in a portfolio optimisation problem, formulated as a multi-stage stochastic integer programme. To approximate the value of this optimisation problem we present a transparent valuation algorithm based on simulation and parametric regression that explicitly takes into account the state variable's multidimensional resource component. We operationalise this approach using three numerical examples of increasing complexity: an American put option in a simple single-factor setting; a natural resource investment with a switching option in a one-factor setting; and the same investment in a three-factor setting. Subsequently, we demonstrate the ability of the proposed approach to evaluate a complex natural resource investment that features both a large portfolio of interdependent real options and four underlying uncertainties. We show how our approach can be used to investigate the way in which the value of that portfolio and its individual real options are affected by the underlying operating margin and the degrees of different uncertainties. Lastly, we extend this approach to include endogenous, decision- and state-dependent uncertainties. We present an efficient valuation algorithm that is more transparent than those used in existing approaches; by exploiting the problem structure it explicitly accounts for the path dependencies of the state variables. The applicability of the extended approach to complex investment projects is illustrated by valuing an urban infrastructure investment. We show the way in which the optimal value of the portfolio and its single, well-defined options are affected by the initial operating revenues, and by the degrees of exogenous and endogenous uncertainty.Open Acces

Pricing Bermudan options under Merton jump-diffusion asset dynamics

In this paper, a recently developed regression-based option pricing method, the Stochastic Grid Bundling Method (SGBM), is considered for pricing multidimensional Bermudan options.We compare SGBM with a traditional regression-based pricing approach and present detailed insight in the application of SGBM, including how to configure it and how to reduce the uncertainty of its estimates by control variates. We consider the Merton jump-diffusion model, which performs better than the geometric Brownian motion in modelling the heavy-tailed features of asset price distributions. Our numerical tests show that SGBM with appropriate set-up works highly satisfactorily for pricing multidimensional options under jump-diffusion asset dynamics

Optimal Decision-Making under Uncertainty - Application to Power Transmission Investments

Economists define investment as the act of incurring immediate costs with the expectation of future returns. An investment project, as every asset has a value. For successfully investing in and managing these assets is crucial not only recognizing what the value is but also the sources of this value. Most investment decisions share three characteristics in different degrees. First, investments are partially or totally irreversible. Roughly speaking, the initial investment cost is at least partially sunk; i.e. it is impossible to recover all the expenditures if the decision-maker changes his mind. Second, there is uncertainty in the revenues from the investment, and therefore, risk associated with this. Third, all decision-making has some leeway about the timing of the investment. It is possible to defer the decision making to get more information about the future. These three features interact to determine the optimal decisions of investors on a given investment project. Transmission utilities are faced with investment projects, which hold these three characteristics: irreversibility, uncertainty and the choice of timing. In this context, an efficient decision making process is, therefore, based on managing the uncertainties and understanding the relationships between risks and opportunities in order to achieve a well-timed investment execution. Therefore, strategic flexibility for seizing opportunities and cutting losses contingent upon the market evolution is of huge value. Strategic flexibility is a risk management method that is gaining ongoing research attention as it enables properly managing major uncertainties, which are unsolved at the time of making decisions. Hence, valuing added flexibility in transmission investment portfolios, for instance, by investing in power electronic-based controller meanwhile transmission line projects are deferred, is necessary to make optimal network upgrading. Nevertheless, expressing the value of flexibility in economic terms is not a trivial task and requires new, sophisticated valuing tools, since the traditional investment theory has not recognized the important implications of the interaction between the three aforementioned investment features. Any attempt to quantify investment flexibility almost naturally leads to the concept of Real Options (RO). The RO technique provides a well-founded framework –based on the theory of financial options, and consequently, stochastic dynamic programming- to assess strategic investments under uncertainty. In the first RO applications, valuation was normally confined to the investment options that can be easily assimilated to financial options, for which solutions are well-known and readily available. Nevertheless, an investor confront with a diverse set of opportunities. From this point of view, investment projects can be seen as a portfolio of options, where its value is driven by several stochastic variables. The introduction of multiple interacting options into real options models highly increases the problem complexity, making traditional numerical approaches impracticable. However in the recent years, simulation procedures for solving multiple American options have been successfully proposed. One of the most promising approaches is the Least Square Monte Carlo (LSM) method proposed by Longstaff and Schwartz in 2001. LSM method is based on stochastic chronological simulation and uses least squares linear regression to determine the optimal stopping time (optimal path) in the decision making process. This chapter lays out a general background about key concepts -uncertainty and risk- and the most usual risk management techniques in transmission investment are provided. Then, the concept of strategic flexibility is introduced in order to set its ability for dealing with the uncertainties involved in the investment problem. In addition, new criteria and advantages of ROV approach compared with classical probabilistic choice are presented, by exposing a LSM-based method for decomposing and evaluating the complex real option problem involved in flexible transmission investments under uncertainties. The proposed methodology is applied in a study case which evaluates an interconnection reinforcement on the European interconnected power system, by showing how the valuation of flexibility is a key task for making efficient and well-timed investments in the transmission network. The impact of two network upgrades on the system-wide welfare is analyzed. These upgrades are the development of a new interconnected line and the installation of a power electronic-based controller. Both upgrades represent measures to strengthen the German-Dutch interconnections due to the fact that these are among the most important corridors within the Central Western European (CWE) region. Hence, an interconnection project, which is currently under study, is compared to flexible investment in order to shed some light on the influence of the strategic flexibility on the optimal decision-making process. The research is focused on assessing the impact of different wind power in-feed scenarios in detail as well as the uncertainty of the demand growth, generation cost evolution and the installed wind capacity on the decision-making process. The presented approach might serve as a basis for a decision-making tool for regulatory agencies in order to quantify the necessity for network upgrades.Fil: Blanco, Gerardo. Universidad Nacional de Asunción; ParaguayFil: Olsina, Fernando Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Ingeniería. Instituto de Energía Eléctrica; Argentin

A Hedged Monte Carlo Approach to Real Option Pricing

In this work we are concerned with valuing optionalities associated to invest or to delay investment in a project when the available information provided to the manager comes from simulated data of cash flows under historical (or subjective) measure in a possibly incomplete market. Our approach is suitable also to incorporating subjective views from management or market experts and to stochastic investment costs. It is based on the Hedged Monte Carlo strategy proposed by Potters et al (2001) where options are priced simultaneously with the determination of the corresponding hedging. The approach is particularly well-suited to the evaluation of commodity related projects whereby the availability of pricing formulae is very rare, the scenario simulations are usually available only in the historical measure, and the cash flows can be highly nonlinear functions of the prices.Comment: 25 pages, 14 figure