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A Cautionary Note on the Put-Call Parity under an Asset Pricing Model with a Lower Reflecting Barrier

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  • Markus Hertrich
Abstract
The put-call parity is free from distributional assumptions. It is tempting to assume that this parity also holds when an asset pricing model includes reflecting barriers. This paper shows that in the case of geometric Brownian motion with reflection such barriers cause the standard put-call parity to differ from the riskneutral parity. This paper then analyzes the error that arises when the diffusion is bounded and the standard put-call parity is applied in a risk-neutral framework as a shortcut to impute put prices from call prices, and vice versa. The risk-neutral parity that is derived for a reflected geometric Brownian motion is then used to analyze the impact that the Swiss National Bank’s minimum exchange rate regime vis-à-vis the euro has had on foreign exchange hedging costs. The analysis shows that in the analyzed period domestic investors may have incurred substantial costs as a result of hedging exposure to the euro currency and may have been overexposed to foreign exchange risk.

Suggested Citation

  • Markus Hertrich, 2015. "A Cautionary Note on the Put-Call Parity under an Asset Pricing Model with a Lower Reflecting Barrier," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 151(III), pages 227-260, September.
    • Handle: RePEc:ses:arsjes:2015-iii-2
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    References listed on IDEAS

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    1. Dumas, Bernard & Svensson, Lars E. O., 1994. "How long do unilateral target zones last?," Journal of International Economics, Elsevier, vol. 36(3-4), pages 467-481, May.
    2. Longstaff, Francis A, 1995. "Option Pricing and the Martingale Restriction," The Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1091-1124.
    3. Unknown, 1985. "1985 March," CWAE Newsletter, Agricultural and Applied Economics Association, Committee on Women in Agricultural Economics (CWAE), pages 1-10, March.
    4. Markus Hertrich & Heinz Zimmermann, 2017. "On the Credibility of the Euro/Swiss Franc Floor: A Financial Market Perspective," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 49(2-3), pages 567-578, March.
    5. Frédéric Bossens & Grégory Rayée & Nikos S. Skantzos & Griselda Deelstra, 2010. "Vanna-Volga Methods Applied To Fx Derivatives: From Theory To Market Practice," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(08), pages 1293-1324.
    6. Ofek, Eli & Richardson, Matthew & Whitelaw, Robert F., 2004. "Limited arbitrage and short sales restrictions: evidence from the options markets," Journal of Financial Economics, Elsevier, vol. 74(2), pages 305-342, November.
    7. Campa, Jose M. & Chang, P. H. Kevin & Reider, Robert L., 1998. "Implied exchange rate distributions: evidence from OTC option markets1," Journal of International Money and Finance, Elsevier, vol. 17(1), pages 117-160, February.
    8. Anonymous, 0. "1983 March," CWAE Newsletter, Agricultural and Applied Economics Association, Committee on Women in Agricultural Economics (CWAE).
    9. Markus Hertrich & Dirk Veestraeten, 2013. "Valuing Stock Options When Prices are Subject to a Lower Boundary: A Correction," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(9), pages 889-890, September.
    10. Campa, Jose Manuel & Chang, P H Kevin, 1996. "Arbitrage-Based Tests of Target-Zone Credibility: Evidence from ERM Cross-Rate Options," American Economic Review, American Economic Association, vol. 86(4), pages 726-740, September.
    11. Anonymous & Loehman, Edna, 0. "1984 March," CWAE Newsletter, Agricultural and Applied Economics Association, Committee on Women in Agricultural Economics (CWAE).
    12. Alessandro Fiori Maccioni, 2011. "Endogenous Bubbles in Derivatives Markets: The Risk Neutral Valuation Paradox," Papers 1106.5274, arXiv.org, revised Sep 2011.
    13. Robert A. Jarrow, 2015. "Asset Price Bubbles," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 201-218, December.
    14. Broome, Simon, 2001. "The lifetime of a unilateral target zone: some extended results," Journal of International Money and Finance, Elsevier, vol. 20(3), pages 419-438, June.
    15. Dirk Veestraeten, 2013. "Currency option pricing in a credible exchange rate target zone," Applied Financial Economics, Taylor & Francis Journals, vol. 23(11), pages 951-962, June.
    16. Unknown, 1987. "1987 March," CWAE Newsletter, Agricultural and Applied Economics Association, Committee on Women in Agricultural Economics (CWAE), pages 1-12, March.
    17. Satchell, Stephen, 2007. "Forecasting Expected Returns in the Financial Markets," Elsevier Monographs, Elsevier, edition 1, number 9780750683210.
    18. Zhiguang Wang & Robert T. Daigler, 2011. "The performance of VIX option pricing models: Empirical evidence beyond simulation," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(3), pages 251-281, March.
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    Cited by:

    1. Dean Buckner & Kevin Dowd & Hardy Hulley, 2022. "Arbitrage Problems with Reflected Geometric Brownian Motion," Papers 2201.05312, arXiv.org, revised Sep 2022.
    2. R. Guy Thomas, 2023. "Long-term option pricing with a lower reflecting barrier," Papers 2302.05808, arXiv.org.

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    More about this item

    Keywords

    Euro/Swiss franc floor; hedging; put-call parity; reflected geometric Brownian motion; risk-neutral parity;
    All these keywords.

    JEL classification:

    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies
    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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