Optimisation, Econometric and Financial Analysis pp 251-271 | Cite as
Real Options with Random Controls, Rare Events, and Risk-to-Ruin
Conference paper
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-ChainsPreview
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References
- Amin, K. I. (1993). Jump diffusion option valuation in discrete time. Journal of Finance, XLVIII, 1833–1863.CrossRefADSGoogle Scholar
- 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
- 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
- Bardham, I., & Chao, X. (1996). On Martingale measures when asset prices have unpredictable jumps. Stochastic Processes and their Applications, 63, 35–54.CrossRefMathSciNetGoogle Scholar
- Bates, S. D. (1991). The crash of ‘87: Was it expected? The evidence from options markets. Journal of Finance, XLVI, 1009–1044.CrossRefGoogle Scholar
- Bergman, Y. Z., Grundy B. D., & Wiener Z. (1996). General properties of option prices. Journal of Finance, 51, 1573–1610.CrossRefGoogle Scholar
- Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–659.CrossRefGoogle Scholar
- 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
- Brynjolffson, E., & Hitt, L. M. (2000). Beyond computation: Information technology, organizational transformation and business performance. Journal of Economic Perspectives, 14, 23–48.CrossRefGoogle Scholar
- 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
- Chan, T. (1999). Pricing contingent claims on stocks driven by Levy processes. Annals of Applied Probability, 9, 504–528.MATHCrossRefMathSciNetGoogle Scholar
- Constantinides, G. (1978). Market risk adjustment in project valuation. Journal of Finance, 33, 603–616.CrossRefGoogle Scholar
- Cox, J., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7, 229–263.CrossRefGoogle Scholar
- Dixit, A. K., & Pindyck, R. S. (1994). Investment Under Uncertainty. Princeton, New Jersey: Princeton University Press.Google Scholar
- Henderson, V., & Hobson, D. (2003). Coupling and option price comparisons under a jump-diffusion model. Stochastics and Stochastic Reports, 75, 79–101.CrossRefMathSciNetGoogle Scholar
- Jarrow, R., & Rudd, A. (1983). Option Pricing. Homewood, Ill.: Richard D. Irwin, Inc.Google Scholar
- Jones, E. P. (1984). Option arbitrage and strategy with large price changes. Journal of Financial Economics, 13, 91–113.CrossRefGoogle Scholar
- Kou, S. G. (2002). A jump diffusion model for option pricing. Management Science, 48, 1086–1101.CrossRefGoogle Scholar
- Kou, S. G., & Wang, H. (2004). Option pricing under a double exponential jump diffusion model. Management Science, 50, 1178–1192.CrossRefGoogle Scholar
- Kushner, H. J. (1977). Probability Methods for Approximations in Stochastic Control and for Elliptic Equations. New York, New York: Academic Press.MATHGoogle Scholar
- Kushner, H. J. (1990). Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems. Cambridge, MA: Birkhäuser Boston.MATHGoogle Scholar
- 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
- Martzoukos, S. H. (2000). Real options with random controls and the value of learning. Annals of Operations Research, 99, 305–323.MATHCrossRefMathSciNetGoogle Scholar
- Martzoukos, S. H. (2003). Multivariate contingent claims on foreign assets following jump-diffusion processes. Review of Derivatives Research, 6, 27–46.MATHCrossRefGoogle Scholar
- 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
- 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
- McDonald, R., & Siegel, D. (1986). The value of waiting to invest. Quarterly Journal of Economics, 101, 707–727.CrossRefGoogle Scholar
- Merton, R. C. (1973). An intertemporal capital asset pricing model. Econometrica, 41, 867–887.MATHCrossRefMathSciNetGoogle Scholar
- Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3, 125–144.CrossRefGoogle Scholar
- Stoll, H. R., & Whaley, R. E. (1993). Futures and Options: Theory and Applications. Cincinnati, Ohio: South-Western Publishing Co.Google Scholar
- 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
- Trigeorgis, L. (1996). Real Options: Managerial Flexibility and Strategy in Resource Allocation. Cambridge, Massachusetts: The MIT Press.Google Scholar
- Vollert, A. (2003). A Stochastic Control Framework for Real Options in Strategic Valuation. Boston: Birkhäuser.Google Scholar
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