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

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  • Jérôme B. Detemple

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  • Suresh Sundaresan
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    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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    Bibliographic Info

    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;

    References

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    1. Jennifer Carpenter, 1997. "The Optimal Dynamic Investment Policy for a Fund Manager Compensated with an Incentive Fee," New York University, Leonard N. Stern School Finance Department Working Paper Seires 97-11, New York University, Leonard N. Stern School of Business-.
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    3. He, Hua, 1990. "Convergence from Discrete- to Continuous-Time Contingent Claims Prices," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 523-46.
    4. 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.
    5. Jennifer Carpenter, 1997. "The Exercise and Valuation of Executive Stock Options," New York University, Leonard N. Stern School Finance Department Working Paper Seires 97-10, New York University, Leonard N. Stern School of Business-.
    6. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
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    Cited by:
    1. Jianjun Miao & Neng Wang, 2006. "Investment, consumption and hedging under incomplete markets," 2006 Meeting Papers 289, Society for Economic Dynamics.
    2. 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.
    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.
    4. Zvi Bodie & J�r�me Detemple & Marcel Rindisbacher, 2009. "Life-Cycle Finance and the Design of Pension Plans," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 249-286, November.
    5. Wei Xiong & Ronnie Sircar, 2004. "Evaluating Incentive Options," Econometric Society 2004 North American Winter Meetings 253, Econometric Society.
    6. Hall, Brian J. & Murphy, Kevin J., 2002. "Stock options for undiversified executives," Journal of Accounting and Economics, Elsevier, vol. 33(1), pages 3-42, February.
    7. J. Scheinkman & C. Rogers L., 2003. "Optimal Exercise of American Claims When," Princeton Economic Theory Working Papers 77e0e688f3178298289e06d42, David K. Levine.
    8. Hamza Bahaji, 2011. "Incentives from stock option grants: a behavioral approach," Post-Print halshs-00681611, HAL.
    9. Bahaji, Hamza, 2014. "Are Employee Stock Option Exercise Decisions Better Explained through the Prospect Theory?," Economics Papers from University Paris Dauphine 123456789/13098, Paris Dauphine University.
    10. Brian J. Hall & Thomas A. Knox, 2002. "Managing Option Fragility," NBER Working Papers 9059, National Bureau of Economic Research, Inc.

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