A Remark on Gatheral's 'Most-Likely Path Approximation' of Implied Volatility

IF 0.4 4区经济学 Q4 BUSINESS, FINANCE

Journal of Derivatives Pub Date : 2009-11-03 DOI:10.2139/ssrn.1499082

Martin Keller-Ressel, J. Teichmann

引用次数: 3

Abstract

We give a new proof of the representation of implied volatility as a time-average of weighted expectations of local or stochastic volatility. With this proof we clarify the question of existence of 'forward implied variance' in the original derivation of Gatheral, who introduced this representation in his book 'The Volatility Surface'.

查看原文本刊更多论文

对隐含波动率的“最可能路径近似”的评述

给出了隐含波动率表示为局部波动率或随机波动率加权期望的时间平均值的新证明。通过这个证明，我们澄清了在Gatheral的原始推导中“前向隐含方差”的存在问题，他在他的书“波动面”中引入了这种表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Derivatives Economics, Econometrics and Finance-Economics and Econometrics

CiteScore

1.30

自引率

14.30%

发文量

期刊介绍： The Journal of Derivatives (JOD) is the leading analytical journal on derivatives, providing detailed analyses of theoretical models and how they are used in practice. JOD gives you results-oriented analysis and provides full treatment of mathematical and statistical information on derivatives products and techniques. JOD includes articles about: •The latest valuation and hedging models for derivative instruments and securities •New tools and models for financial risk management •How to apply academic derivatives theory and research to real-world problems •Illustration and rigorous analysis of key innovations in derivative securities and derivative markets