A PDE Method for Estimation of Implied Volatility
29 Pages Posted: 2 Nov 2018 Last revised: 24 Nov 2019
Date Written: October 10, 2018
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
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