BUBBLES, CONVEXITY AND THE BLACK-SCHOLES EQUATION
成果类型：
Article
署名作者：
Ekstrom, Erik; Tysk, Johan
署名单位：
Uppsala University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/08-AAP579
发表日期：
2009
页码：
1369-1384
关键词：
摘要：
A bubble is characterized by the presence of an underlying asset whose discounted price process is a strict local martingale under the pricing measure. In such markets, many standard results from option pricing theory do not hold, and in this paper we address some of these issues. In particular, we derive existence and uniqueness results for the Black-Scholes equation, and we provide convexity theory for option pricing and derive related ordering results with respect to volatility. We show that American options are convexity preserving, whereas European options preserve concavity for general payoffs and convexity only for bounded contracts.