Extremes of stochastic volatility models

• 成果类型: Article
• 署名作者: Breidt, FJ; Davis, RA
• 署名单位: Iowa State University; Colorado State University System; Colorado State University Fort Collins
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 1998
• 页码: 664-675
• 关键词: bayesian-analysis; Weak Convergence; random-variables; variance; options

摘要

Extreme value theory for a class of stochastic volatility models, in which the logarithm of the conditional variance follows a Gaussian linear process, is developed. A result for the asymptotic tail behavior of the transformed stochastic volatility process is established and used to prove that the suitably normalized extremes converge in distribution to the double exponential (Gumbel) distribution. Explicit normalizing constants are obtained, and point process convergence is discussed.