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

Hertrich, Markus

doi:10.1007/bf03399417

Cited by 6 publications

(13 citation statements)

References 57 publications

(87 reference statements)

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“…This expression, and also equation (2) for the put in the main paper and their difference in equation (A.9), all look slightly different to those inHertrich (2015), because he defines some of the z variates differently in that paper. His z 3 is my z 2 , and his z 4 is my -z 3 + σ √ T. I am using the variates as defined inHertrich & Zimmerman (2017).…”

mentioning

confidence: 82%

“…Hertrich & Zimmermann (2017) consider a put on an exchange rate; this version is the one directly adapted for the present paper. Hertrich (2015) gives a fuller account of the derivation, leading to the same formula but with the terms grouped in a slightly different way, and also gives a more technical discussion of the put-call parity issue than my intuitive treatment in Appendix B. The working paper Hertrich & Zimmermann (2015) gives some of the necessary integrals.…”

Section: Appendix a Derivation Of The Put Option Pricing Formulamentioning

confidence: 99%

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Valuation of no-negative-equity guarantees with a lower reflecting barrier

Thomas

2020

Ann. actuar. sci.

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Abstract If the general level of house prices falls a long way, policymakers may introduce new policies which seek to support prices. This paper considers the effect of such interventions on the valuation of no-negative-equity guarantees (NNEG) in equity release mortgages. I model interventions by a reflecting barrier expressed as a fraction of the current level of house prices. Reflection at the barrier is instantaneous, so the no-arbitrage property is preserved, and hence risk-neutral valuation of NNEG is possible. The reflecting barrier can alternatively be justified as a representation of the different economic nature of the underlying housing (and particularly freehold land) assets in NNEG valuations, compared with the underlying equity assets in many other option valuations.

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confidence: 82%

Section: Appendix a Derivation Of The Put Option Pricing Formulamentioning

confidence: 99%

Valuation of no-negative-equity guarantees with a lower reflecting barrier

Thomas

2020

Ann. actuar. sci.

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“…Such a process is obtained by applying Skorokhod's (1961) construction to a vanilla geometric Brownian motion, causing it to reflect off a lower boundary. Veestraeten (2013), Hertrich (2015), and Hertrich and Zimmermann (2017) have used RGBMs to model exchange rates constrained by central bank target zone policies, while Thomas (2021) recently modelled house prices as an RGBM, under the assumption that the government will support the property market if prices fall enough. Veestraeten (2008) claimed that the RGBM model does not offer any arbitrage opportunities.…”

Section: Introductionmentioning

confidence: 99%

“…He then obtained an expression for the density of the putative equivalent risk-neutral probability measure and used it to derive pricing formulae for European puts and calls. With some modifications to cater for dividends, and following an amendment to the put pricing formula by Hertrich and Veerstraeten (2013), Veestraeten's (2008) option pricing formulae have been used by Veestraeten (2013), Hertrich (2015), Hertrich and Zimmermann (2017) and Thomas (2021).…”

Section: Introductionmentioning

confidence: 99%

Arbitrage Problems with Reflected Geometric Brownian Motion

Buckner¹,

Dowd²,

Hulley³

2022

Preprint

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Contrary to the claims made by several authors, a financial market model in which the price of a risky security follows a reflected geometric Brownian motion is not arbitrage-free.In fact, such a model is unsuitable for contingent claim valuation because it violates even the weakest no-arbitrage conditions. In particular, it does not admit a well-defined market price of risk, let alone a numéraire portfolio or an equivalent risk-neutral probability measure. Moreover, the published option pricing formulae for such models violate textbook no-arbitrage bounds.

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“…For a detailed discussion on put-call parity when reflection is superimposed on GBM, seeHertrich (2015).…”

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confidence: 99%

Foreign Exchange Interventions Under a One-Sided Target Zone Regime and the Swiss Franc

Hertrich

2020

SSRN Journal

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From September 2011 to January 2015, the Swiss National Bank (SNB) implemented a minimum exchange rate regime (i.e. a one-sided target zone) vis-à-vis the euro to fight deflationary pressures in the aftermath of the Great Financial Crisis. During this period of unconventional monetary policy, the SNB faced mounting criticism from the media and the public on the sizable balance sheet risks that it was incurring. Motivated by this episode, I present a structural model embedded within the target zone framework developed by Krugman (1991) that allows monetary authorities to determine ex-ante the maximum size of foreign exchange market interventions that are expected to be necessary to implement and maintain a one-sided target zone. An empirical application of the proposed model to the aforementioned episode reveals that it is well suited to explain the actual size of these interventions and that, in January 2015, the SNB's euro purchases might indeed have been large without the abandonment of the minimum exchange rate regime, which is consistent with the official statements of the SNB in the aftermath of that episode.

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

Abstract: and three anonymous referees for helpful comments and suggestions that improved the initial version. All remaining errors and omissions remain my responsibility. This work is dedicated to Alma Linnéa.

Cited by 6 publications

References 57 publications

Valuation of no-negative-equity guarantees with a lower reflecting barrier

Valuation of no-negative-equity guarantees with a lower reflecting barrier

Arbitrage Problems with Reflected Geometric Brownian Motion

Foreign Exchange Interventions Under a One-Sided Target Zone Regime and the Swiss Franc

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