Do Standard Real Option Models Overestimate the Required Rate of Return of Real Estate Investment Opportunities?

We consider how the inter-temporal discreteness of the revenue and cost processes affect the optimal timing of a real estate investment opportunity in comparison with the investment timing strategy obtained by relying on the traditional continuous real option model. We characterize both optimal investment rules explicitly and show that the continuous model may lead to a significantly higher required rate of return than the discrete model. Hence, our results show that the use of continuous time models leads to smaller and suboptimal amount of investment. Our numerical illustrations also indicate that this difference grows as volatility increases. Consequently, even though higher volatility decelerates investment in the discrete case as well, it decelerates it less than the continuous model would predict.Real options, real estate investment timing, exchange option

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

On the problems of sequential statistical inference for Wiener processes with delayed observations

We study the sequential hypothesis testing and quickest change-point (or disorder) detection problems with linear delay penalty costs for observable Wiener processes under (constantly) delayed detection times. The method of proof consists of the reduction of the associated delayed optimal stopping problems for one-dimensional diffusion processes to the equivalent free-boundary problems and solution of the latter problems by means of the smooth-fit conditions. We derive closed-form expressions for the Bayesian risk functions and optimal stopping boundaries for the associated weighted likelihood ratio processes in the original problems of sequential analysis

The Effects of Implementation Delay on Decision-Making Under Uncertainty

In this paper, we accomplish two objectives: First, we provide a new mathematical characterization of the value function for impulse control problems with implementation delay and present a direct solution method that differs from its counterparts that use quasi-variational inequalities. Our method is direct, in the sense that we do not have to guess the form of the solution and we do not have to prove that the conjectured solution satisfies conditions of a verification lemma. Second, by employing this direct solution method, we solve two examples that involve decision delays: an exchange rate intervention problem and a problem of labor force optimization

Impulse control problem on finite horizon with execution delay

We consider impulse control problems in finite horizon for diffusions with decision lag and execution delay. The new feature is that our general framework deals with the important case when several consecutive orders may be decided before the effective execution of the first one. This is motivated by financial applications in the trading of illiquid assets such as hedge funds. We show that the value functions for such control problems satisfy a suitable version of dynamic programming principle in finite dimension, which takes into account the past dependence of state process through the pending orders. The corresponding Bellman partial differential equations (PDE) system is derived, and exhibit some peculiarities on the coupled equations, domains and boundary conditions. We prove a unique characterization of the value functions to this nonstandard PDE system by means of viscosity solutions. We then provide an algorithm to find the value functions and the optimal control. This easily implementable algorithm involves backward and forward iterations on the domains and the value functions, which appear in turn as original arguments in the proofs for the boundary conditions and uniqueness results

On investment, uncertainty, and strategic interaction with applications in energy markets

The thesis presents dynamic models on investment under uncertainty with the focus on strategic interaction and energy market applications. The uncertainty is modelled using stochastic processes as state variables. The specific questions analyzed include the effect of technological and revenue related uncertainties on the optimal timing of investment, the irreversibility in the choice between alternative investment projects with different degrees of uncertainty, and the effect of strategic interaction on the initiating of discrete investment projects, on the abandonment of a project, and on incremental capacity investments. The main methodological feature is the incorporation of game theoretic concepts in the theory of investment. It is argued that such an approach is often desirable in terms of real applications, because many industries are characterized by both uncertainty and strategic interaction between the firms. Besides extending the theory of investment, this line of work may be seen as an extension of the theory of industrial organization towards the direction that views market stability as one of the factors explaining rational behaviour of the firms.reviewe