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Optimal Hedging and Valuation of Nontraded Assets

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  • Lucie Teplå

Abstract

This paper examines a number of valuation problems faced by an expected-utility maximizing investor who, over a given time horizon, is constrained to hold an asset which cannot be replicated by dynamic trading and which therefore does not have a unique no-arbitrage price. We first derive the private valuation which the investor assigns to the nontraded asset in order to determine his optimal investment in the traded assets. We thereby show that, as part of this portfolio, the investor hedges the private valuation process of the nontraded asset, rather than its market price process. We also study the price at which the investor would be willing to sell the nontraded asset if he were subsequently prohibited from trading in it, as well as the amount the investor would be willing to pay to remove the trading restriction. All three values are shown to depend in an intuitive manner on the investor’s risk aversion, the residual risk of the nontraded asset unhedged by the traded assets, the difference between the constrained holding and optimal unconstrained holding of the asset and the length of the time horizon over which the asset cannot be traded. JEL Classification: G11

Suggested Citation

  • Lucie Teplå, 2000. "Optimal Hedging and Valuation of Nontraded Assets," Review of Finance, European Finance Association, vol. 4(3), pages 231-251.
    • Handle: RePEc:oup:revfin:v:4:y:2000:i:3:p:231-251.
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    File URL: http://hdl.handle.net/10.1023/A:1011454223409
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    Cited by:

    1. John H. Cochrane, 2014. "A Mean-Variance Benchmark for Intertemporal Portfolio Theory," Journal of Finance, American Finance Association, vol. 69(1), pages 1-49, February.
    2. Jianmin Shi, 2020. "Optimal control of multiple Markov switching stochastic system with application to portfolio decision," Papers 2010.16102, arXiv.org.
    3. Daniele Marazzina, 2024. "Optimal retirement in presence of stochastic labor income: a free boundary approach in presence of an incomplete market," Papers 2407.19190, arXiv.org.
    4. Rubtsov, Alexey, 2016. "Model misspecification and pricing of illiquid claims," Finance Research Letters, Elsevier, vol. 18(C), pages 242-249.
    5. Jianmin Shi, 2023. "Dynamic asset allocation with multiple regime‐switching markets," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(2), pages 1741-1755, April.
    6. Alain Bensoussan & Bong-Gyu Jang & Seyoung Park, 2016. "Unemployment Risks and Optimal Retirement in an Incomplete Market," Operations Research, INFORMS, vol. 64(4), pages 1015-1032, August.
    7. Rubtsov, Alexey & Xu, Wei & Šević, Aleksandar & Šević, Željko, 2021. "Price of climate risk hedging under uncertainty," Technological Forecasting and Social Change, Elsevier, vol. 165(C).
    8. Vicky Henderson, 2005. "The impact of the market portfolio on the valuation, incentives and optimality of executive stock options," Quantitative Finance, Taylor & Francis Journals, vol. 5(1), pages 35-47.

    More about this item

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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