Financial options and statistical prediction intervals

• 成果类型: Article
• 署名作者: Mykland, PA
• 署名单位: University of Chicago
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1065705113
• 发表日期: 2003
• 页码: 1413-1438
• 关键词: stochastic volatility; diffusion-coefficient; prices; DECOMPOSITION; FUTURE; models

摘要

The paper shows how to convert statistical prediction sets into worst case hedging strategies for derivative securities. The prediction sets can, in particular, be ones for volatilities and correlations of the underlying securities, and for interest rates. This permits a transfer of statistical conclusions into prices for options and similar financial instruments. A prime feature of our results is that one can construct the trading strategy as if the prediction set had a 100% probability. If, in fact, the set has probability 1 - alpha, the hedging strategy will work with at least the same probability. Different types of prediction regions are considered. The starting value A(0) for the trading strategy corresponding to the 1 - alpha prediction region is a form of long term value at risk. At the same time, A(0) is coherent.