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

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  • 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.

Suggested Citation

  • Jérôme B. Detemple & Suresh Sundaresan, 1999. "Non-Traded Asset Valuation with Portfolio Constraints: A Binomial Approach," CIRANO Working Papers 99s-08, CIRANO.
  • Handle: RePEc:cir:cirwor:99s-08
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    File URL: http://www.cirano.qc.ca/files/publications/99s-08.pdf
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    References listed on IDEAS

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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. Carpenter, Jennifer N., 1998. "The exercise and valuation of executive stock options," Journal of Financial Economics, Elsevier, vol. 48(2), pages 127-158, May.
    4. 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..
    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 247-257, August.
    6. He, Hua, 1990. "Convergence from Discrete- to Continuous-Time Contingent Claims Prices," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 523-546.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Tung-Hsiao Yang & Don M. Chance, 2014. "The Price-Taker Effect On The Valuation Of Executive Stock Options," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 37(1), pages 27-54, February.
    4. Rubtsov, Alexey, 2016. "Model misspecification and pricing of illiquid claims," Finance Research Letters, Elsevier, vol. 18(C), pages 242-249.
    5. Vicky Henderson & Kamil Klad'ivko & Michael Monoyios, 2017. "Executive stock option exercise with full and partial information on a drift change point," Papers 1709.10141, arXiv.org.
    6. repec:dau:papers:123456789/13098 is not listed on IDEAS
    7. Miao, Jianjun & Wang, Neng, 2007. "Investment, consumption, and hedging under incomplete markets," Journal of Financial Economics, Elsevier, vol. 86(3), pages 608-642, December.
    8. Andrew Ang & Nicolas P.B. Bollen, 2010. "Locked Up by a Lockup: Valuing Liquidity as a Real Option," Financial Management, Financial Management Association International, vol. 39(3), pages 1069-1096, September.
    9. Kimura, Toshikazu, 2010. "Valuing executive stock options: A quadratic approximation," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1368-1379, December.
    10. Wei Xiong & Ronnie Sircar, 2004. "Evaluating Incentive Options," Econometric Society 2004 North American Winter Meetings 253, Econometric Society.
    11. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    12. 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.
    13. Zvi Bodie & Jérôme 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.
    14. J. Scheinkman & C. Rogers L., 2003. "Optimal Exercise of American Claims When," Princeton Economic Theory Working Papers 77e0e688f3178298289e06d42, David K. Levine.
    15. Brian J. Hall & Thomas A. Knox, 2002. "Managing Option Fragility," NBER Working Papers 9059, National Bureau of Economic Research, Inc.
    16. Hamza Bahaji, 2011. "Incentives from stock option grants: a behavioral approach," Post-Print halshs-00681611, HAL.

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