A new unbiased additive robust volatility estimation using extreme values of asset prices
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A new unbiased additive robust volatility estimation using extreme values of asset prices Muneer Shaik1,2
· S. Maheswaran1
© Swiss Society for Financial Market Research 2020
Abstract We propose a new unbiased robust volatility estimator based on extreme values of asset prices. We show that the proposed Add Extreme Value Robust Volatility Estimator (AEVRVE) is unbiased and is 2–3 times more efficient relative to the Classical Robust Volatility Estimator (CRVE). We put forth a novel procedure to remove the downward bias present in the data even without increasing the number of steps in the stock price path. We perform Monte Carlo simulation experiments to show the properties of unbiasedness and efficiency. The proposed estimator remains exactly unbiased relative to the standard robust volatility estimator in the empirical data based on global stock indices namely CAC 40, DOW, IBOVESPA, NIKKEI, S&P 500 and SET 50. Keywords Robust volatility ratio · Efficiency · Bias · Volatility estimators · Monte Carlo simulation · Extreme values of asset prices JEL Classification C51 · C58 · G10
1 Introduction An asset’s volatility acts as a measure of risk and plays a vital role in many areas of economics and finance. Most of the research on volatility in the area of financial econometrics can be classified into three broad areas: (1) estimation of volatility, (2) modeling volatility, and (3) forecasting volatility. Since volatility is unobservable and is stochastic in nature, a precise and accurate estimation of volatility is essential for modeling and forecasting. In this paper, we focus on and contribute to the literature
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Muneer Shaik [email protected] S. Maheswaran [email protected]
1
Institute for Financial Management and Research, Chennai 600034, India
2
IFMR Graduate School of Business, Krea University, Sri City 517646, India
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M. Shaik, S. Maheswaran
on the first and foremost problem in measuring volatility, that is, its estimation, by proposing a new unbiased robust volatility estimator based on extreme values of asset prices. Consider asset returns over N number of days. Typically, the average daily return (or mean) of a stock over N number of days will be approximately equal to zero. The variance, in general, is the standard proxy for measuring volatility, which explains how much the asset returns change over a period of time. The variance is easily calculated by taking the average of the squared (demeaned) daily returns, when we have only the closing prices of a day. This estimate of volatility, that is, the variance, is very noisy and might not be sufficient because the volatility changes from one day to the next. The volatility models in the literature apply time series techniques by first estimating the volatility by taking the squared returns, since the variance is the most common and often used volatility estimate. The dispersion of the stock prices can also be measured using absolute returns. Though the use of absolute returns as a volatility proxy is very limited, it has significant advant
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