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The Stop-Loss Start-Gain Paradox and Option Valuation: A New Decomposition into Intrinsic and Time Value

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  • Carr, Peter P
  • Jarrow, Robert A

Abstract

The downside risk in a leveraged stock position can be eliminated by using stop-loss orders. The upside potential of such a position can be captured using contingent buy orders. The terminal payoff to this stop-loss start-gain strategy is identical to that of a call option, but the strategy costs less initially. This article resolves this paradox by showing that the strategy is not self-financing for continuous stock- price processes of unbounded variation. The resolution of the paradox leads to a new decomposition of an option's price into its intrinsic and time value. When stock price follows geometric Brownian motion, this decomposition is proven to be mathematically equivalent to the Black-Scholes (1973) formula. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

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Bibliographic Info

Article provided by Society for Financial Studies in its journal Review of Financial Studies.

Volume (Year): 3 (1990)
Issue (Month): 3 ()
Pages: 469-92

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Handle: RePEc:oup:rfinst:v:3:y:1990:i:3:p:469-92

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Cited by:
  1. Mark Broadie & Jérôme B. Detemple, 1996. "American Options on Dividend-Paying Assets," CIRANO Working Papers 96s-16, CIRANO.
  2. Nicolas Perkowski & David J. Pr\"omel, 2014. "Local times for typical price paths and pathwise Tanaka formulas," Papers 1405.4421, arXiv.org.
  3. A. Bellier-Delienne, 2005. "Synthèse sur les Options de Livraison dans les Contrats à Terme," THEMA Working Papers 2005-09, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  4. A. M. G. Cox & David Hobson & Jan Ob{\l}\'oj, 2007. "Pathwise inequalities for local time: Applications to Skorokhod embeddings and optimal stopping," Papers math/0702173, arXiv.org, revised Nov 2008.
  5. Kraft, Holger, 2007. "Pitfalls in static superhedging of barrier options," Finance Research Letters, Elsevier, vol. 4(1), pages 2-9, March.
  6. Zhi Guo & Eckhard Platen, 2011. "The Small and Large Time Implied Volatilities in the Minimal Market Model," Papers 1109.6154, arXiv.org, revised Oct 2011.
  7. Joon Y. Park, 2004. "The Spatial Analysis of Time Series," Econometric Society 2004 North American Winter Meetings 595, Econometric Society.
  8. Salopek, D. M., 2002. "A new class of nearly self-financing strategies," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 69-75, January.
  9. J. Scheinkman & W. Xiong, 2002. "Overconfidence, Short-Sale Constraints and Bubbles," Princeton Economic Theory Working Papers 98734966f1c1a57373801367f, David K. Levine.
  10. Jarrow, Robert & Protter, Philip, 2012. "Discrete versus continuous time models: Local martingales and singular processes in asset pricing theory," Finance Research Letters, Elsevier, vol. 9(2), pages 58-62.
  11. Aleksandar Mijatović, 2010. "Local time and the pricing of time-dependent barrier options," Finance and Stochastics, Springer, vol. 14(1), pages 13-48, January.

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