APPROXIMATING STOCHASTIC VOLATILITY BY RECOMBINANT TREES

• 成果类型: Article
• 署名作者: Akyildirim, Erdinc; Dolinsky, Yan; Soner, H. Mete
• 署名单位: Borsa Istanbul; Swiss Federal Institutes of Technology Domain; ETH Zurich; Hebrew University of Jerusalem
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP977
• 发表日期: 2014
• 页码: 2176-2205
• 关键词: pricing american options; limit

摘要

A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov process. The first two components are related to the stock and volatility processes and take values in a two-dimensional binomial tree. The other two components of the Markov process are the increments of random walks with simple values in {-1, +1}. The resulting efficient option pricing equations are numerically implemented for general American and European options including the standard put and calls, bather, lookback and Asian-type pay-offs. The weak and extended weak convergences are also proved.