A generalized complementarity approach to solving real option problems

Journal of Economic Dynamics and Control

Volumn 32, Issue 6, 2008, Pages 1754-1779

  Nagae, Takeshi ^a   Akamatsu, Takashi ^b  

^a KOBE UNIVERSITY   (Japan)

^b TOHOKU UNIVERSITY   (Japan)

Author keywords

Generalized complementarity problem; Real options; Smoothing function based algorithm

Indexed keywords

EID: 43849084021     PISSN: 01651889     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jedc.2007.04.010     Document Type: Article

References (47)

1. Akamatsu, T., Nagae, T., 2007. Option graphs: evaluating complex interdependent decisions under uncertainty. Management Science, submitted for publication.
2. Amin K., and Khanna A. Convergence of American option values from discrete- to continuous-time financial models. Mathematical Finance 4 (1994) 289-304
3. Bar-Ilan A., and Strange W.C. Investment lags. American Economic Review 86 (1996) 610-622
4. Bar-Ilan A., Sulem A., and Zanello A. Time-to-build and capacity choice. Journal of Economic Dynamics & Control 26 (2002) 69-98
5. Barone-Adesi G., and Whaley R. Efficient analytical approximation of American option values. Journal of Finance 42 (1987) 301-320
6. Ben-Akiva M., and Lerman S.R. Discrete Choice Analysis: Theory and Application to Travel Demand (1985), MIT Press, Cambridge
7. Bensoussan A. On the theory of option pricing. Acta Applicandae Mathematicae 2 (1984) 39-158
8. Boyle P. A lattice framework for option pricing with two state variables. Journal of Financial and Quantitative Analysis 23 (1988) 1-12
9. Brennan M.J., and Schwartz E.S. The valuation of American put options. The Journal of Finance 32 (1977) 449-462
10. Brennan M.J., and Schwartz E.S. Evaluating natural resource investments. Journal of Business 58 (1985) 135-157
11. Broadie M., and Detemple J. American option valuation: new bounds, approximations, and a comparison of existing methods. The Review of Financial Studies 9 (1996) 1211-1250
12. Coleman T.F., Li Y., and Verma A. A Newton method for American option pricing. Journal of Computational Finance 5 (2002) 51-78
13. Cottle R.W., and Dantzig G.B. A generalization of the linear complementarity problem. Journal of Combinatorial Theory 8 (1970) 79-90
14. Cox J.C., Ross S.A., and Rubinstein M. Option pricing: a simplified approach. Journal of Financial Economics 7 (1979) 229-263
15. Daganzo C.F. Multinomial Probit: The Theory and its Application to Demand Forecasting (1979), Academic Press, New York
16. Dempster M., and Hutton J. Pricing American stock options by linear programming. Mathematical Finance 9 (1999) 229-254
17. Detemple J., and Tian W. The valuation of American options for a class of diffusion processes. Management Science 48 (2002) 917-937
18. Dixit A.K. Entry and exit decisions under uncertainty. Journal of Political Economy 97 (1989) 620-638
19. Dixit A.K., and Pindyck R.S. Investment under Uncertainty (1994), Princeton University Press, Princeton
20. Duffie D. Dynamic Asset Pricing Theory. second ed (1996), Princeton University Press, Princeton
21. Ferris M.C., and Pang J.-S. Engineering and economic applications of complementarity problems. SIAM Review 39 (1997) 669-713
22. Geske R., and Johnson H. The American put option valued analytically. Journal of Finance 39 (1984) 1511-1524
23. Huang J., and Pang J.-S. Option pricing and linear complementarity. Journal of Computational Finance 2 (1998) 31-60
24. Hull J. Options, Futures and Other Derivative Securities (1989), Princeton-Hall, Englewood Cliffs, NJ
25. Jacka S. Optimal stopping and the American put. Mathematical Finance 1 (1991) 1-14
26. Jaillet P., Lamberton D., and Lapeyre B. Variational inequalities and the pricing of American options. Acta Applicandae Mathmaticae 21 (1990) 263-289
27. Karatzas I. On the pricing of American options. Applied Mathematics and Optimization 17 (1988) 37-60
28. Kim I. The analytic valuation of American options. The Review of Financial Studies 3 (1990) 547-572
29. Kulatilaka N. The value of flexibility: a general model of real options. In: Trigeorgis L. (Ed). Real Options in Capital Investment (1995), Praeger, New York
30. Kulatilaka N., and Trigeorgis L. The general flexibility to switch: Real options revisited. International Journal of Finance 6 (1994) 778-798
31. Lamberton D. Error estimates for the binomial approximation of American put options. The Annals of Applied Probability 8 (1998) 206-233
32. Leisen D.P.J. Pricing the American put option: a detailed convergence analysis for binomial models. Journal of Economic Dynamics & Control 22 (1998) 1419-1444
33. MacMillan L.W. An analytic approximation for the American put price. Advances in Futures and Option Research 1 (1986) 119-139
34. Majd S., and Pindyck R.S. Time to build, option value, and investment decisions. Journal of Financial Economics 18 (1987) 7-17
35. Malchow-Møller N., and Thorsen B.J. Repeated real options: optimal investment behaviour and a good rule of thumb. Journal of Economic Dynamics & Control 29 (2005) 1025-1041
36. McDonald R., and Siegel D. Investment and the valuation of firms when there is an option to shut down. International Economic Review 26 (1985) 331-349
37. McFadden D.L. Conditional logit analysis of qualitative choice behaviour. In: Zarembka P. (Ed). Frontiers in Econometrics (1974), Academic Press, New York
38. McKean Jr. H.P. Appendix: A free boundary problem for the heat equation arising from a problem in mathematical economics. Industrial Management Review 6 (1965) 32-39
39. Milne A., and Whalley A.E. Time to build, option value and investment decisions: a comment. Journal of Financial Economics 56 (2000) 325-332
40. Myneni R. The pricing of American option. The Annals of Applied Probability 2 (1992) 1-23
41. Peng J.-M. A smoothing function and its applications. In: Fukushima M., and Qi L. (Eds). Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods (1999), Kluwer Academic Publishers, Dordrecht 293-316
42. Peng J.-M., and Lin Z. A non-interior continuation method for generalized linear complementarity problem. Mathematical Programming 86 (1999) 533-563
43. Qi H.-D., and Liao L.-Z. A smoothing Newton method for extended vertical linear complementarity problem. SIAM Journal on Matrix Analysis and Applications 21 (1999) 45-66
44. In: Schwartz E.S., and Trigeorgis L. (Eds). Real Options and Investment under Uncertainty - Classical Readings and Recent Contributions (2001), MIT Press, Cambridge
45. Trigeorgis L. A log-transformed binomial numerical analysis method for valuing complex multi-option investments. Journal of Financial and Quantitative Analysis 26 (1991) 309-326
46. Trigeorgis L. The nature of option interactions and the valuation of investments with multiple real options. Journal of Financial and Quantitative Analysis 28 (1993) 1-20
47. Wilmott P., Dewynne J.N., and Howison S. Option Pricing: Mathematical Models and Computation (1993), Oxford Financial Press, Oxford, United Kingdom