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Volatility estimation from observed option prices

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  • Phelim P. Boyle
  • Draviam Thangaraj

Abstract

It is well established that the standard Black-Scholes model does a very poor job in matching the prices of vanilla European options. The implied volatility varies by both time to maturity and by the moneyness of the option. One approach to this problem is to use the market option prices to back out a local volatility function that reproduces the market prices. Since option price observations are only available for a limited set of maturities and strike prices, most algorithms require a smoothing technique to implement this approach. In this paper we modify the implementation of Andersen and Brotherton-Ratcliffe to provide another way of dealing with this issue. Numerical examples indicate that our approach is reasonably successful in reproducing the input prices.

Suggested Citation

  • Phelim P. Boyle & Draviam Thangaraj, 2000. "Volatility estimation from observed option prices," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 23(1), pages 31-52.
    • Handle: RePEc:spr:decfin:v:23:y:2000:i:1:p:31-52
    Note: Received: 22 December 1999
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    Cited by:

    1. Kim, Sangkwon & Kim, Junseok, 2021. "Robust and accurate construction of the local volatility surface using the Black–Scholes equation," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Andrew Na & Meixin Zhang & Justin Wan, 2023. "Computing Volatility Surfaces using Generative Adversarial Networks with Minimal Arbitrage Violations," Papers 2304.13128, arXiv.org, revised Dec 2023.
    3. U Hou Lok & Yuh‐Dauh Lyuu, 2020. "Efficient trinomial trees for local‐volatility models in pricing double‐barrier options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(4), pages 556-574, April.

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