二阶渐近隐含波动率及其在SABR模型中的应用

IF 0.4 4区经济学 Q4 BUSINESS, FINANCE

Journal of Derivatives Pub Date : 2009-06-03 DOI:10.2139/ssrn.1413649

L. Paulot

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引用次数: 93

摘要

我们提供了一种计算随机波动率模型隐含波动率的泰勒展开式的一般方法，使用热核展开式。除了已知的0阶隐含波动率外，我们从热核膨胀的标量系数中精确地计算出一阶修正。此外，热核展开的第一次修正给出了隐含波动率的第二次修正，我们也准确地给出了所有打击。作为应用，我们计算了SABR模型的二阶渐近展开式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Asymptotic Implied Volatility at the Second Order with Application to the SABR Model

We provide a general method to compute a Taylor expansion in time of implied volatility for stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is already known, we compute the first order correction exactly at all strikes from the scalar coefficient of the heat kernel expansion. Furthermore, the first correction in the heat kernel expansion gives the second order correction for implied volatility, which we also give exactly at all strikes. As an application, we compute this asymptotic expansion at order 2 for the SABR model.

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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