Real Options with Random Controls, Rare Events, and Risk-to-Ruin

  • Nicos Koussis
  • Spiros H. Martzoukos
  • Lenos Trigeorgis
Conference paper
Part of the Advances in Computational Management Science book series (AICM, volume 9)

Summary

Situations involving real investment options in the presence of multiple sources of jump risk, and controls are analyzed. Randomly arriving jumps include also the special cases of jump-to-ruin on the underlying asset, or on the contingent claim. Management has available impulse-type controls with random outcome. The analytic solutions when available, and a Markov-Chain numerical approach for solving more general investment decision problems are demonstrated

Key words

Flexibility real options multi-class jump-diffusion processes catastrophic risks controls with random outcome Markov-Chains 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amin, K. I. (1993). Jump diffusion option valuation in discrete time. Journal of Finance, XLVIII, 1833–1863.CrossRefADSGoogle Scholar
  2. Andersen, L., & Andreasen, J. (2001). Jump-diffusion processes: Volatility smile fitting and numerical methods for option pricing. Review of Derivatives Research, 4, 231–262.CrossRefGoogle Scholar
  3. Ball, C.A., & Torous W. N. (1985). On jumps in common stock prices and their impact on call option pricing. Journal of Finance, XL, 155–173.CrossRefGoogle Scholar
  4. Bardham, I., & Chao, X. (1996). On Martingale measures when asset prices have unpredictable jumps. Stochastic Processes and their Applications, 63, 35–54.CrossRefMathSciNetGoogle Scholar
  5. Bates, S. D. (1991). The crash of ‘87: Was it expected? The evidence from options markets. Journal of Finance, XLVI, 1009–1044.CrossRefGoogle Scholar
  6. Bergman, Y. Z., Grundy B. D., & Wiener Z. (1996). General properties of option prices. Journal of Finance, 51, 1573–1610.CrossRefGoogle Scholar
  7. Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–659.CrossRefGoogle Scholar
  8. Brennan, M. J. (1991). The price of convenience and the valuation of commodity contingent claims. In D. Lund, & B. Øksendal, (Eds.), Stochastic Models and Option Values. (pp. 33–72). Amsterdam, Netherlands: North-Holland.Google Scholar
  9. Brynjolffson, E., & Hitt, L. M. (2000). Beyond computation: Information technology, organizational transformation and business performance. Journal of Economic Perspectives, 14, 23–48.CrossRefGoogle Scholar
  10. Bunch, D. S., & Smiley, R. (1992). Who deters entry? Evidence on the use of strategic entry deterrents. Review of Economics and Statistics, 74, 509–521.CrossRefGoogle Scholar
  11. Chan, T. (1999). Pricing contingent claims on stocks driven by Levy processes. Annals of Applied Probability, 9, 504–528.MATHCrossRefMathSciNetGoogle Scholar
  12. Constantinides, G. (1978). Market risk adjustment in project valuation. Journal of Finance, 33, 603–616.CrossRefGoogle Scholar
  13. Cox, J., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7, 229–263.CrossRefGoogle Scholar
  14. Dixit, A. K., & Pindyck, R. S. (1994). Investment Under Uncertainty. Princeton, New Jersey: Princeton University Press.Google Scholar
  15. Henderson, V., & Hobson, D. (2003). Coupling and option price comparisons under a jump-diffusion model. Stochastics and Stochastic Reports, 75, 79–101.CrossRefMathSciNetGoogle Scholar
  16. Jarrow, R., & Rudd, A. (1983). Option Pricing. Homewood, Ill.: Richard D. Irwin, Inc.Google Scholar
  17. Jones, E. P. (1984). Option arbitrage and strategy with large price changes. Journal of Financial Economics, 13, 91–113.CrossRefGoogle Scholar
  18. Kou, S. G. (2002). A jump diffusion model for option pricing. Management Science, 48, 1086–1101.CrossRefGoogle Scholar
  19. Kou, S. G., & Wang, H. (2004). Option pricing under a double exponential jump diffusion model. Management Science, 50, 1178–1192.CrossRefGoogle Scholar
  20. Kushner, H. J. (1977). Probability Methods for Approximations in Stochastic Control and for Elliptic Equations. New York, New York: Academic Press.MATHGoogle Scholar
  21. Kushner, H. J. (1990). Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems. Cambridge, MA: Birkhäuser Boston.MATHGoogle Scholar
  22. Kushner, H. J., & DiMasi, G. (1978). Approximations for functionals and optimal control on jump diffusion processes. Journal of Mathematical Analysis and Applications, 40, 772–800.CrossRefMathSciNetGoogle Scholar
  23. Martzoukos, S. H. (2000). Real options with random controls and the value of learning. Annals of Operations Research, 99, 305–323.MATHCrossRefMathSciNetGoogle Scholar
  24. Martzoukos, S. H. (2003). Multivariate contingent claims on foreign assets following jump-diffusion processes. Review of Derivatives Research, 6, 27–46.MATHCrossRefGoogle Scholar
  25. Martzoukos, S. H., & Trigeorgis, L. (2002). Real (investment) options with multiple types of rare events. European Journal of Operational Research, 136, 696–706.MATHCrossRefMathSciNetGoogle Scholar
  26. McDonald, R., & Siegel, D. (1984). Option pricing when the underlying asset earns a below-equilibrium rate of return: A note. Journal of Finance, 39, 261–265.CrossRefGoogle Scholar
  27. McDonald, R., & Siegel, D. (1986). The value of waiting to invest. Quarterly Journal of Economics, 101, 707–727.CrossRefGoogle Scholar
  28. Merton, R. C. (1973). An intertemporal capital asset pricing model. Econometrica, 41, 867–887.MATHCrossRefMathSciNetGoogle Scholar
  29. Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3, 125–144.CrossRefGoogle Scholar
  30. Stoll, H. R., & Whaley, R. E. (1993). Futures and Options: Theory and Applications. Cincinnati, Ohio: South-Western Publishing Co.Google Scholar
  31. Trigeorgis, L. (1993). The nature of option interactions and the valuation of investments with multiple real options. Journal of Financial and Quantitative Analysis, 28, 1–20.CrossRefGoogle Scholar
  32. Trigeorgis, L. (1996). Real Options: Managerial Flexibility and Strategy in Resource Allocation. Cambridge, Massachusetts: The MIT Press.Google Scholar
  33. Vollert, A. (2003). A Stochastic Control Framework for Real Options in Strategic Valuation. Boston: Birkhäuser.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Nicos Koussis
    • 1
  • Spiros H. Martzoukos
    • 1
  • Lenos Trigeorgis
    • 1
  1. 1.Department of Public and Business AdministrationUniversity of CyprusNicosiaCyprus

Personalised recommendations