Pricing and hedging in incomplete markets

• 成果类型: Article
• 署名作者: Carr, P; Geman, H; Madan, DB
• 署名单位: University System of Maryland; University of Maryland College Park; New York University; Universite PSL; Universite Paris-Dauphine; ESSEC Business School
• 刊物名称: JOURNAL OF FINANCIAL ECONOMICS
• ISSN/ISSBN: 0304-405X
• DOI: 10.1016/S0304-405X(01)00075-7
• 发表日期: 2001
• 页码: 131-167
• 关键词: Risk management; state price density; unique Martingale measure; complete markets; option pricing

摘要

We present a new approach for positioning, pricing, and hedging in incomplete markets that bridges standard arbitrage pricing and expected utility maximization. Our approach for determining whether an investor should undertake a particular position involves specifying a set of probability measures and associated floors which expected payoffs must exceed in order for the investor to consider the hedged and financed investment to be acceptable. By assuming that the liquid assets are priced so that each portfolio of assets has negative expected return under at least one measure, we derive a counterpart to the first fundamental theorem of asset pricing. We also derive a counterpart to the second fundamental theorem, which leads to unique derivative security pricing and hedging even though markets are incomplete. For products that are not spanned by the liquid assets of the economy, we show how our methodology provides more realistic bid-ask spreads. (C) 2001 Published by Elsevier Science S.A.