STATE PRICE DENSITY ESTIMATION VIA NONPARAMETRIC MIXTURES

• 成果类型: Article
• 署名作者: Yuan, Ming
• 署名单位: University System of Georgia; Georgia Institute of Technology
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/09-AOAS246
• 发表日期: 2009
• 页码: 963-984
• 关键词: CONTINGENT CLAIMS; implicit

摘要

We consider nonparametric estimation of the state price density encapsulated in option prices. Unlike usual density estimation problems, we only observe option prices and their corresponding strike prices rather than samples from the state price density. We propose to model the state price density directly with a nonparametric mixture and estimate it using least squares. We show that although the minimization is taken over an infinitely dimensional function space, the minimizer always admits a finite dimensional representation and can be computed efficiently. We also prove that the proposed estimate of the state price density function converges to the truth at a nearly parametric rate.