A PDE Method for Estimation of Implied Volatility

29 Pages Posted: 2 Nov 2018 Last revised: 24 Nov 2019

See all articles by Ivan Matic

Ivan Matic

CUNY Baruch College

Rados Radoicic

CUNY Baruch College

Dan Stefanica

Baruch College, City University of New York

Date Written: October 10, 2018

Abstract

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.

Keywords: Implied Volatility, Partial Differential Equations, Numerical Approximation, Black-Scholes Model, Bachelier Model

JEL Classification: C63, C88

Suggested Citation

Matic, Ivan and Radoicic, Rados and Stefanica, Dan, A PDE Method for Estimation of Implied Volatility (October 10, 2018). Available at SSRN: https://ssrn.com/abstract=3264356 or http://dx.doi.org/10.2139/ssrn.3264356

Ivan Matic

CUNY Baruch College ( email )

17 Lexington Avenue
New York, NY 10021
United States

Rados Radoicic (Contact Author)

CUNY Baruch College ( email )

One Bernard Baruch Way
New York, NY 10010
United States

Dan Stefanica

Baruch College, City University of New York ( email )

One Bernard Baruch Way
New York, NY 10010
United States

HOME PAGE: http://mfe.baruch.cuny.edu/dan-stefanica

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