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Semi-efficient valuations and put-call parity
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Herdegen, Martin and Schweizer, Martin (2018) Semi-efficient valuations and put-call parity. Mathematical Finance, 28 (4). pp. 1061-1106. doi:10.1111/mafi.12162
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Official URL: http://doi.org/10.1111/mafi.12162
Abstract
We propose an approach to the valuation of payoffs in general semimartingale models of financial markets where prices are nonnegative. Each asset price can hit 0; we only exclude that this ever happens simultaneously for all assets. We start from two simple, economically motivated axioms, namely absence of arbitrage (in the sense of NUPBR) and absence of relative arbitrage among all buy-and-hold strategies (called static efficiency). A valuation process for a payoff is then called semi-efficient consistent if the financial market enlarged by that process still satisfies this combination of properties. It turns out that this approach lies in the middle between the extremes of valuing by risk-neutral expectation and valuing by absence of arbitrage alone. We show that this always yields put-call parity, although put and call values themselves can be nonunique, even for complete markets. We provide general formulas for put and call values in complete markets and show that these are symmetric and that both contain three terms in general. We also show that our approach recovers all the put-call parity respecting valuation formulas in the
classic theory as special cases, and we explain when and how the different terms in the put and call valuation formulas disappear or simplify. Along the way, we also
define and characterize completeness for general semimartingale financial markets and connect this to the classic theory.
| Item Type: | Journal Article | |||||||||
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| Subjects: | H Social Sciences > HG Finance Q Science > QA Mathematics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||
| Library of Congress Subject Headings (LCSH): | Options (Finance) -- Mathematical models., Hedging (Finance) -- Mathematical models., Probabilities., Options (Finance) -- Prices. | |||||||||
| Journal or Publication Title: | Mathematical Finance | |||||||||
| Publisher: | Wiley-Blackwell Publishing, Inc. | |||||||||
| ISSN: | 0960-1627 | |||||||||
| Official Date: | October 2018 | |||||||||
| Dates: |
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| Volume: | 28 | |||||||||
| Number: | 4 | |||||||||
| Page Range: | pp. 1061-1106 | |||||||||
| DOI: | 10.1111/mafi.12162 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Grant number: | 105218_150101 | |||||||||
| RIOXX Funder/Project Grant: |
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| Open Access Version: |
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