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December 2019 Nonparametric spot volatility from options
Viktor Todorov
Ann. Appl. Probab. 29(6): 3590-3636 (December 2019). DOI: 10.1214/19-AAP1488

Abstract

We propose a nonparametric estimator of spot volatility from noisy short-dated option data. The estimator is based on forming portfolios of options with different strikes that replicate the (risk-neutral) conditional characteristic function of the underlying price in a model-free way. The separation of volatility from jumps is done by making use of the dominant role of the volatility in the conditional characteristic function over short time intervals and for large values of the characteristic exponent. The latter is chosen in an adaptive way in order to account for the time-varying volatility. We show that the volatility estimator is near rate-optimal in minimax sense. We further derive a feasible joint central limit theorem for the proposed option-based volatility estimator and existing high-frequency return-based volatility estimators. The limit distribution is mixed Gaussian reflecting the time-varying precision in the volatility recovery.

Citation

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Viktor Todorov. "Nonparametric spot volatility from options." Ann. Appl. Probab. 29 (6) 3590 - 3636, December 2019. https://doi.org/10.1214/19-AAP1488

Information

Received: 1 November 2017; Revised: 1 November 2018; Published: December 2019
First available in Project Euclid: 7 January 2020

zbMATH: 07172342
MathSciNet: MR4047988
Digital Object Identifier: 10.1214/19-AAP1488

Subjects:
Primary: 60E10, 60F05
Secondary: 60J60, 60J75

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 6 • December 2019
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