Henderson, Vicky and Hobson, David (David G.). (2008) Perpetual American options in incomplete markets : the infinitely divisible case. Quantitive Finance, Vol.8 (No.5). pp. 461-469. ISSN 1469-7688

Full text not available from this repository.

Abstract

We consider the exercise of a number of American options in an incomplete market. In this paper we are interested in the case where the options are infinitely divisible. We make the simplifying assumptions that the options have infinite maturity, and the holder has exponential utility. Our contribution is to solve this problem explicitly and we show that, except at the initial time when it may be advantageous to exercise a positive fraction of his holdings, it is never optimal for the holder to exercise a tranche of options. Instead, the process of option exercises is continuous; however, it is singular with respect to calendar time. Exercise takes place when the stock price reaches a convex boundary which we identify.

Item Type:	Journal Article
Subjects:	H Social Sciences > HB Economic Theory H Social Sciences > HG Finance Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Options (Finance), Markets, Equilibrium (Economics), Distribution (Probability theory)
Journal or Publication Title:	Quantitive Finance
Publisher:	IOP Publishing
ISSN:	1469-7688
Date:	2008
Volume:	Vol.8
Number:	No.5
Number of Pages:	9
Page Range:	pp. 461-469
Identification Number:	10.1080/14697680701400986
Status:	Peer Reviewed
Publication Status:	Published
Funder:	National Science Foundation (U.S.) (NSF), Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	DMI 0447990 (NSF)
References:	Arfken, G., Mathematical Methods for Physicists, 3rd ed., 1985 (Academic Press: New York). Bettis, J.C., Bizjak, J.M. and Lemmon, M.L., Exercise behavior, valuation and the incentive effects of employee stock options. J. Finan. Econ., 2005, 76, 445–470. Carmona, R. and Touzi, N., Optimal multiple stopping and valuation of swing options. Math. Finan., 2004, to appear. Carpenter, J., The exercise and valuation of executive stock options. J. Finan. Econ., 1998, 48, 127–158. Davis, M.H.A., Optimal hedging with basis risk, 2000, Preprint. Davis, M.H.A. and Norman, A.R., Portfolio selection with transactions costs. Math. Oper. Res., 1990, 15, 676–713. Davis, M.H.A. and Zariphopoulou, T., American options and transaction fees, Mathematical Finance IMA Volumes in Mathematics and its Applications, 1995 (Springer: Berlin). Detemple, J. and Sundaresan, S., Nontraded asset valuation with portfolio constraints: a binomial approach. Rev. Finan. Stud., 1999, 12, 835–872. Dixit, A.K. and Pindyck, R.S., Investment under Uncertainty, 1994 (Princeton University Press: Princeton). Grasselli, M., Nonlinearity, correlation and the valuation of employee options, 2005, Preprint. Grasselli, M. and Henderson, V., Risk Aversion, Effort and Block Exercise of Executive Stock Options, 2007, Preprint. Hall, B. and Murphy, K.J., Stock options for undiversified employees. J. Account. Econ., 2002, 33, 3–42. Henderson, V., The impact of the market portfolio on the valuation, incentives and optimality of executive stock options. Quant. Finan., 2005, 5, 35–47. Henderson, V., Valuing the option to invest in an incomplete market. Math. Finan. Econ., 2007, 1, 103–128. Henderson, V. and Hobson, D., A note on irreversible investment, hedging and optimal consumption problems. Int. J. Theor. Appl. Finan., 2006, 9, 997–1007. Henderson, V. and Hobson, D., Horizon unbiased utility functions. Stochast. Process. Applic., 2007a, 11, 1621–1641. Henderson, V. and Hobson, D., Utility indifference pricing: an overview. In Indifference Pricing, edited by R. Carmona, 2007b (Princeton University Press: Princeton), to appear. Hodges, S. and Neuberger, A., Optimal replication of contingent claims under transactions costs. Rev. Fut. Mkts., 1989, 8, 222–239. Huddart, S. and Lang, M., Employee stock option exercises: an empirical analysis. J. Account. Econ., 1996, 21, 5–43. Jain, A. and Subramanian, A., The intertemporal exercise and valuation of employee stock options. Account. Rev., 2004, 79, 705–743. Karatzas, I. and Kou, S.G., Hedging American contingent claims with constrained portfolios. Finan. Stochast., 1998, 2, 215–258. Karatzas, I. and Wang, H., Utility maximization with discretionary stopping. SIAM J. Control Optim., 2001, 39, 306–329. McDonald, R. and Siegel, D.R., The value of waiting to invest. Q. J. Econ., 1986, 101, 707–727. McKean, H.P., A free boundary problem for the heat equation arising from a problem in mathematical economics. Ind. Mgmt Rev., 1965, 6, 32–39 (Appendix to Samuelson P.A., 1965, Rational theory of warrant pricing. Ind. Mgmt Rev., 1965, 6, 13–31). Merton, R.C., Theory of rational option pricing. Bell J. Econ. Mgmt, 1973, 4, 141–183. Miao, J. and Wang, N., Investment, consumption and hedging under incomplete markets. J. Finan. Econ., 2006, to appear. Murphy, K.J., Executive compensation, In Handbook of Labor Economics, edited by O. Ashenfelter and D. Card, Vol. 3, 1999 (North-Holland: Amsterdam). Rogers, L.C.G.R. and Scheinkman, J., Optimal exercise of executive stock options, 2006, Preprint. Zariphopoulou, T., A solution approach to valuation with unhedgeable risks. Finan. Stochast., 2001, 5, 61–82.
URI:	http://wrap.warwick.ac.uk/id/eprint/29494

Data sourced from Thomson Reuters' Web of Knowledge

Request changes to a record

Actions (login required)

View Item