Pricing and hedging of Asian options: quasi-explicit solutions via Malliavin calculus

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• 作者：1. School of Finance and Statistics ; Hunan University ; 410079 Changsha ; China2. School of Mathematics and Statistics ; University of Sydney ; Sydney ; NSW 2006 ; Australia3. School of Mathematical Sciences ; Dublin City University ; Collins Avenue ; Glasnevin ; Dublin 9 ; Ireland
• 关键词：Asian options – ; Option pricing – ; Hedging – ; Malliavin calculus
• 刊名：Mathematical Methods of Operations Research (ZOR)
• 出版年：2011
• 出版时间：August 2011
• 年：2011
• 卷：74
• 期：1
• 页码：93-120
• 全文大小：1.0 MB
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• 作者单位：http://www.springerlink.com/content/aj65w62216623844/
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Operation Research and Decision Theory
  Business
  
• 出版者：Physica Verlag, An Imprint of Springer-Verlag GmbH
• ISSN：1432-5217

文摘

We use Malliavin calculus and the Clark–Ocone formula to derive the hedging strategy of an arithmetic Asian Call option in general terms. Furthermore we derive an expression for the density of the integral over time of a geometric Brownian motion, which allows us to express hedging strategy and price of the Asian option as an analytic expression. Numerical computations which are based on this expression are provided.