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Multiscale Volatility Analysis for Noisy High-Frequency Data
Hurst exponent and time-varying intraday volatility
The study of multiscale properties and scaling laws has long been a topic in finance. One of the key questions is: how does the distribution of returns behave at different timescales?
The standard Brownian motion (or random walk) model intrinsically determines the distribution of returns at all time scales due to the independent increments and other model properties. The generalization to fractional Brownian motion (fBm) by Mandelbrot and Van Ness (1968) leads to a much larger class of stochastic processes, allowing for new scaling properties and a long-memory process.
In our new paper, we develop new statistical methods to estimate and analyze the multiscale volatility in asset prices using intraday high-frequency prices.
We analyze a price model with microstructure noise and present a new method to estimate it using real-world high-frequency price data.
The observed price is assumed to be the sum of latent fractional Brownian motion and an independent microstructure noise.
Price = Fractional Brownian Motion + Noise
Interestingly, the multiscale volatility function is not monotonic and there exists a critical timescale minimizing the volatility (see formula here).
We apply real-world data to estimate the volatility and Hurst exponents. Specifically, we consider a collection of exchange-traded funds (ETFs) and stocks (tickers: SPY, IWM, QQQ, XLK, AAPL, and MSFT), with dates ranging from January 2020 to February 2023. For our experiments, we use 3s high-frequency intraday price data. Prices are recorded on each day from open to close, spanning 6.5 hours, making 7800 equal-spaced time points. We choose a time frame such that 𝑡=1 corresponds to 1 min
Fig. 2. shows the multiscale volatility estimated on a 3s intraday price time series. We see that the volatility is clearly not constant across timescales. There is a consistent downward slope…
