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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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    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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