Abstract
One of the most challenging issues in management is the valuation of strategic investments. In particular, when undertaking projects such as an expansion or the launch of a new brand, or an investment in R&D and intellectual capital, which are characterized by a long-term horizon, a firm has also to face the risk due to the interest rate. In this work, we propose to value investments subject to interest rate risk using a real options approach (Schulmerich, 2010). This task requires the typical technicalities of option pricing, which often rely on complex and time-consuming techniques to value investment projects. For instance, Schulmerich (2010) is, to the best of our knowledge, the first work where the interest rate risk is considered for real option analysis. Nevertheless, the valuation of investment projects is done by employing binomial trees, which are computationally very expensive. In the current paper, a different modeling framework (in continuous-time) for real option pricing is proposed which allows one to account for interest rate risk and, at the same time, to reduce computational complexity. In particular, the net present value of the cash inflows is specified by a geometric Brownian motion and the interest rate is modeled by using a process of Vasicek type, which is calibrated to real market data. Such an approach yields an explicit formula for valuing various kinds of investment strategies, such as the option to defer and the option to expand. Therefore, the one proposed is the first model in the field of real options that accounts for the interest rate risk and, at the same time, offers an easy to implement formula which makes the model itself very suitable for practitioners. An empirical analysis is presented which illustrates the proposed approach from the practical point-of-view and highlights the impact of stochastic interest rates in investment valuation.
Highlights
The present paper is devoted to assessing the impact of stochastic interest rates in real option pricing
In order to avoid numerical approximations, we assume that the interest rates follow the popular Vasicek model (Vasicek, 1977) and we manage to price real options using an exact closed-form solution
We apply the formula to the case of real options and to keep the analysis as close as possible to reality we calibrate the parameters of the Vasicek model to the Euribor/Eurirs indexes
Summary
One of the most popular techniques for valuing strategic investments such as an expansion or the launch of a new brand, or an investment in R&D and intellectual capital, is the use of a real options approach (Santos et al, 2014; Kalhagen & Elnegaard, 2002; Manley & Niquidet, 2010; Bernardo et al, 2012; Trang et al,. 2002; Chen et al, 2009; Erbas & Memis, 2012; Gamba & Fusari, 2009; Gibson & Schwartz, 1990; Huchzermeier & Loch, 2001; Liu et al, 2014; Lund, 2005; Paddock et al, 1988; Quigg, 1993; Taş & Ersen, 2012; Williams, 1991). An empirical study is presented in which both the investment cost and the net present value of the future cash inflows depend on the investment date Such an analysis reveals that the stochastic interest rates affect the value of the project, but not the optimal time to invest. The paper is organized as follows: in Section 2 some of the most common examples of real options are described; in Section 3 the basic facts about option pricing under both the Black-Scholes and the Rabinovitch models are recalled; in Section 4 an empirical analysis of the effect of stochastic interest rates is performed; in Section 5 a practical application study is presented; Section 6 discusses the main limitations of the study conducted in the present paper; in Section 7 some conclusions are drawn
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