A PDE method for estimation of implied volatility |
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Authors: | Ivan Matić Dan Stefanica |
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Affiliation: | Baruch College, City University of New York, New York, NY, USA |
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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. |
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Keywords: | Implied volatilities Partial differential equations Numerical methods for option pricing Black–Scholes model Bachelier model |
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