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A PDE method for estimation of implied volatility

Author

Listed:
  • Ivan Matić
  • Radoš Radoičić
  • Dan Stefanica

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.

Suggested Citation

  • Ivan Matić & Radoš Radoičić & Dan Stefanica, 2020. "A PDE method for estimation of implied volatility," Quantitative Finance, Taylor & Francis Journals, vol. 20(3), pages 393-408, March.
    • Handle: RePEc:taf:quantf:v:20:y:2020:i:3:p:393-408
    DOI: 10.1080/14697688.2019.1675898
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