Articlebronze2008

Inference for volatility-type objects and implications for hedging

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Stochastic processes and financial applications Financial Markets and Investment Strategies Financial Risk and Volatility Modeling

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.

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References

1973The Pricing of Options and Corporate Liabilities 1986Generalized autoregressive conditional heteroskedasticity 1982Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation 1973Risk, Return, and Equilibrium: Empirical Tests 1973Theory of Rational Option Pricing 2007Brownian Motion and Stochastic Calculus 2005Theory of rational option pricing 2005Stochastic Integration and Differential Equations

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2003Financial options and statistical prediction intervals 2010A Gaussian calculus for inference from high frequency data 2017Assessment of Uncertainty in High Frequency Data: The Observed Asymptotic Variance 2008Nonparametric Stochastic Volatility 2014Fourier transform methods for pathwise covariance estimation in the presence of jumps 2016Between data cleaning and inference: Pre-averaging and robust estimators of the efficient price

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