Semi-efficient valuations and put-call parity

被引:6
|
作者
Herdegen, Martin [1 ]
Schweizer, Martin [2 ,3 ]
机构
[1] Univ Warwick, Dept Stat, Ramphal Bldg R2-37, Coventry CV4 7AL, W Midlands, England
[2] Swiss Fed Inst Technol, Math, HG G51-2,Ramistr 101, CH-8092 Zurich, Switzerland
[3] Swiss Finance Inst, Walchestr 9, CH-8006 Zurich, Switzerland
基金
瑞士国家科学基金会;
关键词
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; CONTINGENT CLAIMS; FUNDAMENTAL THEOREM; LOCAL MARTINGALES; OPTIONS; ARBITRAGE; MARKETS; BUBBLES; PRICES;
D O I
10.1111/mafi.12162
中图分类号
F8 [财政、金融];
学科分类号
0202 ;
摘要
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.
引用
收藏
页码:1061 / 1106
页数:46
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