Statistics and Its Interface

Volume 1 (2008)

Number 2

Inference for volatility-type objects and implications for hedging

Pages: 255 – 278

DOI: http://dx.doi.org/10.4310/SII.2008.v1.n2.a4

Authors

Per A. Mykland (Department of Statistics, The University of Chicago, Chicago, Il., U.S.A.)

Lan Zhang (Department of Finance, The University of Chicago, Chicago, Il., U.S.A.)

Abstract

The paper studies inference for volatility type objects and its implications for the hedging of options. It considers the nonparametric estimation of volatilities and instantaneous covariations between diffusion type processes. This is then linked to options trading, where we show that our estimates can be used to trade options without reference to the specific model. The new options “delta” becomes an additive modification of the (implied volatility) Black-Scholes delta. The modification, in our example, is both substantial and statistically significant. In the inference problem, explicit expressions are found for asymptotic error distributions, and it is explained why one does not in this case encounter a biasvariance tradeoff, but rather a variance-variance tradeoff. Observation times can be irregular. A non-rigorous extension to estimation under microstructure is provided.

Keywords

volatility estimation, implied volatility, realized volatility, small interval asymptotics, stable convergence, option hedging

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