Practical guide to real options in discrete time II

This paper is an extended version of the paper 'Practical Guide to Real Options in Discrete Time' (http://econwpa.wustl.edu:80/eps/fin/papers/0405/0405016.pdf), where a general, computationally simple approach to real options in discrete time was suggested. We explicitly formulate conditions of the general theorems for basic types of real options, and explain our method in detail for the case of transition density given by exponential functions on each half-axis. To demonstrate that the discrete time approach can be more analytically tractable than the continuous time one, we consider timing of investment with lags, and a model of gradual capital expansion. We obtain simple formulas for the expected values of capital stock in every time period; in continuous time models, a much more sophisticated technique is needed.Real options, embedded options, expected present value operators

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

A class of recursive optimal stopping problems with applications to stock trading

In this paper we introduce and solve a class of optimal stopping problems of recursive type. In particular, the stopping payoff depends directly on the value function of the problem itself. In a multi-dimensional Markovian setting we show that the problem is well posed, in the sense that the value is indeed the unique solution to a fixed point problem in a suitable space of continuous functions, and an optimal stopping time exists. We then apply our class of problems to a model for stock trading in two different market venues and we determine the optimal stopping rule in that case.Comment: 35 pages, 2 figures. In this version, we provide a general analysis of a class of recursive optimal stopping problems with both finite-time and infinite-time horizon. We also discuss other application

Entry-exit decisions with implementation delay under uncertainty

summary:We employ a natural method from the perspective of the optimal stopping theory to analyze entry-exit decisions with implementation delay of a project, and provide closed expressions for optimal entry decision times, optimal exit decision times, and the maximal expected present value of the project. The results in conventional research were obtained under the restriction that the sum of the entry cost and exit cost is nonnegative. In practice, we may meet cases when this sum is negative, so it is necessary to remove the restriction. If the sum is negative, there may exist two trigger prices of entry decision, which does not happen when the sum is nonnegative, and it is not optimal to enter and then immediately exit the project even though it is an arbitrage opportunity