A PDE method for estimation of implied volatility

被引：4

作者：

Matic, Ivan ^{[1
]}

Radoicic, Rados ^{[1
]}

Stefanica, Dan ^{[1
]}

机构：

[1] CUNY, Baruch Coll, New York, NY 10021 USA

来源：

QUANTITATIVE FINANCE | 2020年 / 20卷 / 03期

关键词：

Implied volatilities; Partial differential equations; Numerical methods for option pricing; Black-Scholes model; Bachelier model; STOCHASTIC VOLATILITY; INVERSE PROBLEMS; FORMULA; DEVIATIONS;

D O I：

10.1080/14697688.2019.1675898

中图分类号：

F8 [财政、金融];

学科分类号：

0202 ;

摘要：

In this paper it is proved that the Black-Scholes implied volatility satisfies a second order non-linear partial differential equation. The obtained PDE is then used to construct an algorithm for fast and accurate polynomial approximation for Black-Scholes implied volatility that improves on the existing numerical schemes from literature, both in speed and parallelizability. We also show that the method is applicable to other problems, such as approximation of implied Bachelier volatility.

引用

页码：393 / 408

页数：16

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