Implementing Real Options Valuation under Macroeconomic Risk and Normally Distributed Cash Flows

Year 2024, , 50 - 67, 16.09.2024

Norvald Instefjord Turalay Kenç

https://doi.org/10.33818/ier.1476515

Abstract

The paper highlights the encountered problems in implementing real options under
more realistic assumptions such as business cycle risk and normally distributed cash
flows. The problems considered include (i) estimating empirical distribution of cash
flows from real option investments; (ii) investment decisions across business cycles,
and (iii) calculating the probability of investing with the above stated rich features.
To this end, we estimate operating cash flows of US corporate firms using a Markov
chain model under both geometric and arithmetic Brownian motions assumptions for
cash flows and develop a valuation model of real option with normally distributed
cash flows. Associated investment valuation models incorporating these estimates
reveal that critical cash flow levels significantly differ across models and regimes.

Keywords

Macroeconomic Risk, Regime Switching, Real Options, Arithmetic Brownian Motion, Geometric Brownian Motion

Ethical Statement

Bu çalışmanın, özgün bir çalışma olduğunu; çalışmanın hazırlık, veri toplama, analiz ve bilgilerin sunumu olmak üzere tüm aşamalarından bilimsel etik ilke ve kurallarına uygun davrandığımı; bu çalışma kapsamında elde edilmeyen tüm veri ve bilgiler için kaynak gösterdiğimi ve bu kaynaklara kaynakçada yer verdiğimi; kullanılan verilerde herhangi bir değişiklik yapmadığımı, çalışmanın Committee on Publication Ethics (COPE)' in tüm şartlarını ve koşullarını kabul ederek etik görev ve sorumluluklara riayet ettiğimi beyan ederim. Herhangi bir zamanda, çalışmayla ilgili yaptığım bu beyana aykırı bir durumun saptanması durumunda, ortaya çıkacak tüm ahlaki ve hukuki sonuçlara razı olduğumu bildiririm.

References

• Arnold, M, A. F. Wagner, and R. Westermann (2013). Growth Options, Macroeconomic Conditions, and the Cross Section of Credit Risk. Journal of Financial Economics 107(2), 350-385.
• Bensoussan, A., Z.F. Yan and G. Yin (2012). Threshold-Type Policies for Real Options Using Regime-Switching Models. SIAM Journal on Financial Mathematics 3(1), 667-689.
• Bhamra, H. S., L.A. Kuehn and I. A. Strebulaev (2010a). The Levered Equity Risk Premium and Credit Spreads: A Unified Framework. Review of Financial Studies 23(2), 645-703.
• Bhamra, H. S., L.A. Kuehn and I. A. Strebulaev (2010b). “The Aggregate Dynamics of Capital Structure and Macroeconomic Risk.” Review of Financial Studies 23(12), 4187-4241.
• Bloom, N (2014). “Fluctuations in Uncertainty.” Journal of Economic Perspectives 28(2), 153-176. Bollen, Nicolas P. B. (1998). “Valuing Options in Regime-Switching Models” The Journal of Derivatives 6(1), 38–49.
• Bollen, Nicolas P. B. (1999). Real Options and Product Life Cycles. Management Science 45(5), 670-684.
• Burg, John van der (2018). Stochastic Continuous-Time Cash Flows: A Coupled Linear-Quadratic Model. PhD thesis, New Zealand: Victoria University Wellington.
• Chen, H (2010). Macroeconomic Conditions and the Puzzles of Credit Spreads and Capital Structure. The Journal of Finance 65(6), 2171-2212.
• Dixit, A. and R. S. Pindyck (1994). Investment Under Uncertainty. Princeton University Press. https://press.princeton.edu/books/hardcover/9780691034102/investment-under-uncertainty.
• Driffill, J, T. Kenc and M. Sola (2013). Real Options with Priced Regime Switching Risk. International Journal of Theoretical and Applied Finance 16(5), 1-31.
• Elliott, Robert J, H.Miao, and J.Yu (2009). Investment Timing Under Regime Switching. International Journal of Theoretical and Applied Finance 12(4), 443-463.
• Elliott, Robert J, L. Aggoun and J. B. Moore (1995). Hidden Markov Models: Estimation and Control. Springer-Verlag.
• Guo, X. J. (2001). An Explicit Solution to an Optimal Stopping Problem with Regime Switching. Journal of Applied Probability 38(2), 464-481.
• Guo, X, J. Miao and E. Morellec (2005). Irreversible Investment with Regime Shifts. Journal of Economic Theory 122(1), 37–59.
• Guo, X. J. and Q. Zhang (2004). Closed-Form Solutions for Perpetual American Put Options with Regime Switching. SIAM Journal on Applied Mathematics 64(6), 2034-2049.
• Gutierrez, G, and T. Phillipon (2017). Investmentless Growth: An Empirical Investigation. Brookings Papers on Economic Activity Fall 2017 (Fall), 89-169.
• Harrison, J. M. (2013). Brownian Models of Performance and Control. Cambridge: Cambridge University Press. Hieber, P (2014). First-Passage Times of Regime Switching Models. Statistics & Probability Letters 92, 148-157.
• Jobert, A. and L. C. G. Rogers (2006). Option Pricing with Markov-Modulated Dynamics. SIAM Journal on Control and Optimization 44(6), 2063-2078.
• Leland, H. E. (2007). Financial Synergies and the Optimal Scope of the Firm: Implications for Mergers, Spinoffs, and Structured Finance. The Journal of Finance 62(2), 765-807.
• Liu, J, J. Pan and T. Wang (2005). An Equilibrium Model of Rare-Event Premia and Its Implication for Option Smirks. Review of Financial Studies 18(1), 131-164.
• McDonald, R. and D. Siegel (1986). The Value of Waiting to Invest. Quarterly Journal of Economics 101, 707-727. Myers, S. C. (1977). Determinants of Corporate Borrowing. Journal of Financial Economics 5, 147-175.
• Sarkar, S. (2000). On the Investment Uncertainty Relationship in a Real Options Model. Journal of Economic Dynamics and Control 24(2), 219-225.
• Schwartz, E S. and M. Moon (2000). Rational Pricing of Internet Companies. Financial Analysts Journal 56(3), 62-75.
• Trigeorgis, L (1996). Real Options. MIT Press.
• Wang, Y, C. R Chen and Y. S. Huang (2014). Economic Policy Uncertainty and Corporate Investment: Evidence from China. Pacific-Basin Finance Journal 26, 227-243.