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Leverage Constraints and the Optimal Hedging of Stock and Bond Options

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  • Naik, Vasanttilak
  • Uppal, Raman

Abstract

This paper considers the problem of a financial institution that needs to hedge a stream of state-contingent cash flows while facing borrowing and short-sales restrictions. The study determines analytically the strategy that minimizes the initial cost of hedging the desired cash flow, which is also the upper bound on its market price, and shows that the impact of leverage constraints on the cost of hedging call and put options is significant and, therefore, the biases detected by tests of option pricing models may not represent arbitrage opportunities. The paper also shows that with credit limits, it is optimal to reduce the rate of trading; thus, these constraints need to be recognized when estimating the trading volume generated in replicating contingent payoffs such as portfolio insurance.

Suggested Citation

  • Naik, Vasanttilak & Uppal, Raman, 1994. "Leverage Constraints and the Optimal Hedging of Stock and Bond Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(2), pages 199-222, June.
    • Handle: RePEc:cup:jfinqa:v:29:y:1994:i:02:p:199-222_00
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    Citations

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    Cited by:

    1. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    2. Bergbrant, Mikael C. & Hunter, Delroy M., 2018. "(How) do credit market conditions affect firms' post-hedging outcomes? Evidence from bank lending standards and firms' currency exposure," Journal of Corporate Finance, Elsevier, vol. 50(C), pages 203-222.
    3. Liu Yang & Qing Zhou, 2021. "Leverage constraints and corporate financing decisions," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 61(4), pages 5199-5230, December.
    4. Huang, Kevin X. D., 2002. "On infinite-horizon minimum-cost hedging under cone constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 27(2), pages 283-301, December.
    5. Aliprantis, Charalambos D. & Tourky, Rabee, 2002. "Markets that don't replicate any option," Economics Letters, Elsevier, vol. 76(3), pages 443-447, August.
    6. Korkie, Bob & Nakamura, Mansao & Turtle, Harry J., 2001. "A contingent claim analysis of closed-end fund premia," International Review of Financial Analysis, Elsevier, vol. 10(4), pages 365-394.
    7. Boyle, Phelim & Tian, Weidong, 2008. "The design of equity-indexed annuities," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 303-315, December.
    8. Aliprantis, C. D. & Brown, D. J. & Werner, J., 2000. "Minimum-cost portfolio insurance," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1703-1719, October.
    9. Aliprantis, Charalambos D. & Polyrakis, Yiannis A. & Tourky, Rabee, 2002. "The cheapest hedge," Journal of Mathematical Economics, Elsevier, vol. 37(4), pages 269-295, July.
    10. Chen, Yingshan & Dai, Min & Xu, Jing & Xu, Mingyu, 2015. "Superhedging under ratio constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 250-264.
    11. Valeriy Ryabchenko & Sergey Sarykalin & Stan Uryasev, 2004. "Pricing European Options by Numerical Replication: Quadratic Programming with Constraints," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(3), pages 301-333, September.
    12. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    13. Joao Amaro de Matos & Paula Antao, 2000. "Market illiquidity and the Bid-Ask spread of derivatives," Nova SBE Working Paper Series wp386, Universidade Nova de Lisboa, Nova School of Business and Economics.
    14. Erdnç Akyildirim & Albert Altarovici, 2016. "Partial hedging and cash requirements in discrete time," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 929-945, June.

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