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Non-Traded Asset Valuation with Portfolio Constraints: A Binomial Approach

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Author Info
Jérôme B. Detemple ()
Suresh Sundaresan
Abstract

We provide a simple binomial framework to value American-style derivatives subject to trading restrictions. The optimal investment of liquid wealth is solved simultaneously with the early exercise decision of the non-traded derivative. No-short-sales constraints on the underlying asset manifest themselves in the form of an implicit dividend yield in the risk neutralized process for the underlying asset. One consequence is that American call options may be optimally exercised prior to maturity even when the underlying asset pays no dividends. Applications to executive compensation options are presented. We also analyze non-traded payoffs based on a price that is imperfectly correlated with the price of a traded asset.

Cet article développe un modèle binomial d'évaluation des titres dérivés américains en présence de contraintes d'investissement. Les politiques optimales d'investissement et d'exercice du titre dérivé non-marchandé sont résolues de manière simultanée . La contrainte d'absence de ventes à découvert se manifeste sous forme d'un dividende implicite portant sur le processus neutre au risque de l'actif sous-jacent. Une des conséquences est l'optimalité possible de l'exercice avant l'expiration du contrat même lorsque l'actif sous-jacent ne paye pas de dividendes. Une application à l'évaluation des options de compensation des cadres d'entreprises est présentée. Nous étudions également l'évaluation de titres basés sur un prix qui est imparfaitement corrélé avec le prix d'un actif transigé.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 99s-08.

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Date of creation: 01 Mar 1999
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Handle: RePEc:cir:cirwor:99s-08

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Keywords: American options; executive compensation options; optimal exercise time; portfolio constraints; non-traded asset; private valuation; certainty-equivalent; liquidity; risk aversion; Options américaines; options de compensation de dirigeants; temps d'exercice optimal; contraintes de portefeuille; actif non-marchand; valeur privée; équivalent certain; liquidité; aversion au risque;

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. He, Hua, 1990. "Convergence from Discrete- to Continuous-Time Contingent Claims Prices," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(4), pages 523-46. [Downloadable!] (restricted)
  2. Carpenter, Jennifer N., 1998. "The exercise and valuation of executive stock options1," Journal of Financial Economics, Elsevier, vol. 48(2), pages 127-158, May. [Downloadable!] (restricted)
  3. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring. [Downloadable!] (restricted)
  4. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
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  5. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August. [Downloadable!] (restricted)
  6. Hua He., 1990. "Convergence from Discrete to Continuous Time Contingent Claims Prices," Research Program in Finance Working Papers RPF-199, University of California at Berkeley.
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  1. Wei Xiong & Ronnie Sircar, 2004. "Evaluating Incentive Options," Econometric Society 2004 North American Winter Meetings 253, Econometric Society. [Downloadable!]
  2. L. C. Rogers & Jose A. Scheinkman, 2003. "Optimal Exercise of American Claims When Markets Are Not Complete," Levine's Bibliography 506439000000000114, UCLA Department of Economics. [Downloadable!]
  3. Alfredo Ibáñez, 2005. "Option-Pricing in Incomplete Markets: The Hedging Portfolio plus a Risk Premium-Based Recursive Approach," Computing in Economics and Finance 2005 216, Society for Computational Economics. [Downloadable!]
  4. Vicky Henderson, 2002. "Stock Based Compensation: Firm-specific risk, Efficiency and Incentives," OFRC Working Papers Series 2002fe01, Oxford Financial Research Centre. [Downloadable!]
  5. J. Scheinkman & C. Rogers L., 2003. "Optimal Exercise of American Claims When," Princeton Economic Theory Working Papers 77e0e688f3178298289e06d42, David K. Levine. [Downloadable!]
  6. Brian J. Hall & Kevin J. Murphy, 2000. "Stock Options for Undiversified Executives," NBER Working Papers 8052, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  7. Darsinos, T. & Satchell, S.E., 2002. "On the Valuation of Warrants and Executive Stock Options: Pricing Formulae for Firms with Multiple Warrants/Executive Options," Cambridge Working Papers in Economics 0218, Faculty of Economics, University of Cambridge. [Downloadable!]
  8. Brian J. Hall & Thomas A. Knox, 2002. "Managing Option Fragility," NBER Working Papers 9059, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  9. Junjian Miao & Neng Wang, 2005. "Investment, Consumption and Hedging under Incomplete Markets," Boston University - Department of Economics - Macroeconomics Working Papers Series WP2005-011, Boston University - Department of Economics, revised Sep 2006. [Downloadable!]
    Other versions:
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