Semi‐Efficient Valuations and Put‐Call Parity

46 Pages Posted: 17 Sep 2018

See all articles by Martin Herdegen

Martin Herdegen

University of Warwick - Department of Statistics

Martin Schweizer

ETH Zurich; Swiss Finance Institute

Multiple version iconThere are 2 versions of this paper

Date Written: October 2018

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.

Keywords: absence of arbitrage, completeness, consistent valuation, efficiency, incomplete markets, maximal strategies, NFLVR, NUPBR, option valuation, put‐call parity, risk‐neutral valuation, semi‐efficient markets, viability

Suggested Citation

Herdegen, Martin and Schweizer, Martin, Semi‐Efficient Valuations and Put‐Call Parity (October 2018). Mathematical Finance, Vol. 28, Issue 4, pp. 1061-1106, 2018, Available at SSRN: https://ssrn.com/abstract=3248620 or http://dx.doi.org/10.1111/mafi.12162

Martin Herdegen (Contact Author)

University of Warwick - Department of Statistics ( email )

Coventry CV4 7AL
United Kingdom

Martin Schweizer

ETH Zurich ( email )

Mathematik, HG G51.2
Raemistrasse 101
CH-8092 Zurich
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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