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Universal bad news principle and pricing of options on dividend-paying assets

Listed author(s):
  • Svetlana Boyarchenko
  • Sergei Levendorskii

We solve the pricing problem for perpetual American puts and calls on dividend-paying assets. The dependence of a dividend process on the underlying stochastic factor is fairly general: any non-decreasing function is admissible. The stochastic factor follows a Levy process. This specification allows us to consider assets that pay no dividends at all when the level of the underlying factor (say, the assets of the firm) is too low, and assets that pay dividends at a fixed rate when the underlying stochastic process remains in some range. Certain dividend processes exhibiting mean-reverting features can be modelled as appropriate increasing functions of Levy processes. The payoffs of both the American put and call options can be represented as the expected present value (EPV) of a certain stream of dividends, and we show that the option must be exercised the first time the EPV of this stream with the original process being replaced by the infimum process starting from the current level, becomes positive. Thus, the exercise threshold depends only on the record setting bad news. The results can be applied to the theory of real options as well; as one of possible applications, we consider the problem of incremental capital expansion.

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Paper provided by in its series Papers with number cond-mat/0404108.

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Date of creation: Apr 2004
Handle: RePEc:arx:papers:cond-mat/0404108
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  1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
  2. Abel, Andrew B. & Eberly, Janice C., 1999. "The effects of irreversibility and uncertainty on capital accumulation," Journal of Monetary Economics, Elsevier, vol. 44(3), pages 339-377, December.
  3. Ben S. Bernanke, 1983. "Irreversibility, Uncertainty, and Cyclical Investment," The Quarterly Journal of Economics, Oxford University Press, vol. 98(1), pages 85-106.
  4. Bianca Hilberink & L.C.G. Rogers, 2002. "Optimal capital structure and endogenous default," Finance and Stochastics, Springer, vol. 6(2), pages 237-263.
  5. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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