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Nonparametric spot volatility from options. (English) Zbl 1443.91301
Summary: 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.

91G20 Derivative securities (option pricing, hedging, etc.)
91G10 Portfolio theory
62P05 Applications of statistics to actuarial sciences and financial mathematics
62G05 Nonparametric estimation
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