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Dec 30

Realized Variance Estimation

Posted by abiao at 17:17 | Paper Review | Comments(10) | Reads(13388)
A summary of paper Zero-intelligence realized variance estimation, by Jim Gatheral and Roel C.A. Oomen, published at FINANCE AND STOCHASTICS.

Motivation: Accurate real-time volatility forecasts are needed for many applications, such as the real-time pricing of options and real time risk management of trading positions. In order to generate a forecast however, we first need a good estimate of realized variance. However, Microstructure effects such as bid-ask bounce cause the series of price returns between trades to be autocorrelated so the obvious estimator of realized variance – the sum of squared returns between trades – is very biased. Therefore the contribution of the present paper is to shed some light on these issues with the aim to provide practitioners with firm guidelines on how to obtain efficient and robust realized variance estimates.

Existing sampling methods & comparison: the series of trade prices, (ii) the series of mid-quotes, and (iii) the series of micro-prices formed by linear weighting of the best bid and ask price by market depth. Among these three methods the third one is the least noisy, with sample paths as
micro price for realized variance estimation
The authors also find mid-quote and micro price data are between 40 to 60 times less noisy than trade data (as measured by the microstructure noise variance) leading to an efficiency gain for realized variance estimation of around 50%. Between the mid-quote and micro price, the former is weakly preferred.

Conclusion: based on simulated data from an artificial “zero-intelligence” market that has been shown to mimic some key properties of actual markets, the authors compare a comprehensive set of nineteen realized variance estimators, and concludes that in practice, the best variance estimator is not always the one suggested by theory. In fact, an ad hoc implementation of a subsampling estimator, realized kernel, or maximum likelihood realized variance, delivers the best overall result.

The new micro-prices sampling method used for realized variance estimation is straightforward as a linear equation of bid, ask prices & volume, it is definitely a worth trial given the huge improvement.

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Thanks for letting us know about variance estimation. I really had a lot of questions about this before.
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