Option pricing in the moderate deviations regime

被引：20

作者：

Friz, Peter ^{[1
,2
]}

Gerhold, Stefan ^{[3
]}

Pinter, Arpad ^{[3
]}

机构：

[1] TU, Berlin, Germany

[2] WIAS Berlin, Berlin, Germany

[3] TU Wien, Vienna, Austria

来源：

MATHEMATICAL FINANCE | 2018年 / 28卷 / 03期

基金：

奥地利科学基金会;

关键词：

asymptotics; implied volatility; moderate deviations; option pricing; SMALL-TIME ASYMPTOTICS; IMPLIED VOLATILITY; FUNCTIONALS; DIFFUSION; PRINCIPLE; THEOREM; SMILE;

D O I：

10.1111/mafi.12156

中图分类号：

F8 [财政、金融];

学科分类号：

0202 ;

摘要：

We consider call option prices close to expiry in diffusion models, in an asymptotic regime (moderately out of the money) that interpolates between the well-studied cases of at-the-money and out-of-the-money regimes. First and higher order small-time moderate deviation estimates of call prices and implied volatilities are obtained. The expansions involve only simple expressions of the model parameters, and we show how to calculate them for generic local and stochastic volatility models. Some numerical computations for the Heston model illustrate the accuracy of our results.

引用

页码：962 / 988

页数：27

共 43 条

[1]

[Anonymous], 1991, Graduate Texts in Mathematics

[2]

Bentata A., 2012, PREPRINT

[3] Computing the implied volatility in stochastic volatility models [J].