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
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References
Amin, K. I. (1993). Jump diffusion option valuation in discrete time. Journal of Finance, XLVIII, 1833–1863.
Andersen, L., & Andreasen, J. (2001). Jump-diffusion processes: Volatility smile fitting and numerical methods for option pricing. Review of Derivatives Research, 4, 231–262.
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.
Bardham, I., & Chao, X. (1996). On Martingale measures when asset prices have unpredictable jumps. Stochastic Processes and their Applications, 63, 35–54.
Bates, S. D. (1991). The crash of ‘87: Was it expected? The evidence from options markets. Journal of Finance, XLVI, 1009–1044.
Bergman, Y. Z., Grundy B. D., & Wiener Z. (1996). General properties of option prices. Journal of Finance, 51, 1573–1610.
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–659.
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.
Brynjolffson, E., & Hitt, L. M. (2000). Beyond computation: Information technology, organizational transformation and business performance. Journal of Economic Perspectives, 14, 23–48.
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.
Chan, T. (1999). Pricing contingent claims on stocks driven by Levy processes. Annals of Applied Probability, 9, 504–528.
Constantinides, G. (1978). Market risk adjustment in project valuation. Journal of Finance, 33, 603–616.
Cox, J., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7, 229–263.
Dixit, A. K., & Pindyck, R. S. (1994). Investment Under Uncertainty. Princeton, New Jersey: Princeton University Press.
Henderson, V., & Hobson, D. (2003). Coupling and option price comparisons under a jump-diffusion model. Stochastics and Stochastic Reports, 75, 79–101.
Jarrow, R., & Rudd, A. (1983). Option Pricing. Homewood, Ill.: Richard D. Irwin, Inc.
Jones, E. P. (1984). Option arbitrage and strategy with large price changes. Journal of Financial Economics, 13, 91–113.
Kou, S. G. (2002). A jump diffusion model for option pricing. Management Science, 48, 1086–1101.
Kou, S. G., & Wang, H. (2004). Option pricing under a double exponential jump diffusion model. Management Science, 50, 1178–1192.
Kushner, H. J. (1977). Probability Methods for Approximations in Stochastic Control and for Elliptic Equations. New York, New York: Academic Press.
Kushner, H. J. (1990). Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems. Cambridge, MA: Birkhäuser Boston.
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.
Martzoukos, S. H. (2000). Real options with random controls and the value of learning. Annals of Operations Research, 99, 305–323.
Martzoukos, S. H. (2003). Multivariate contingent claims on foreign assets following jump-diffusion processes. Review of Derivatives Research, 6, 27–46.
Martzoukos, S. H., & Trigeorgis, L. (2002). Real (investment) options with multiple types of rare events. European Journal of Operational Research, 136, 696–706.
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.
McDonald, R., & Siegel, D. (1986). The value of waiting to invest. Quarterly Journal of Economics, 101, 707–727.
Merton, R. C. (1973). An intertemporal capital asset pricing model. Econometrica, 41, 867–887.
Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3, 125–144.
Stoll, H. R., & Whaley, R. E. (1993). Futures and Options: Theory and Applications. Cincinnati, Ohio: South-Western Publishing Co.
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.
Trigeorgis, L. (1996). Real Options: Managerial Flexibility and Strategy in Resource Allocation. Cambridge, Massachusetts: The MIT Press.
Vollert, A. (2003). A Stochastic Control Framework for Real Options in Strategic Valuation. Boston: Birkhäuser.
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Koussis, N., Martzoukos, S.H., Trigeorgis, L. (2007). Real Options with Random Controls, Rare Events, and Risk-to-Ruin. In: Kontoghiorghes, E.J., Gatu, C. (eds) Optimisation, Econometric and Financial Analysis. Advances in Computational Management Science, vol 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36626-1_12
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DOI: https://doi.org/10.1007/3-540-36626-1_12
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