In the previous post, we discussed the close-to-close historical volatility. Recall that the close-to-close historical volatility (CCHV) is calculated as follows, where xi are the logarithmic returns calculated based on closing prices, and N is the sample size. A disadvantage of using the CCHV is that it does not take …

In a previous post, we touched upon a stock’s volatility through its beta. In this post, we are going to discuss historical volatilities of a stock in more details. If you want to use the online version, go to Historical Volatility Online Calculator. Also referred to as statistical volatility, historical …

What is equity (or stock) beta? In finance, beta measures a stock’s volatility with respect to the overall market. It is used in many areas of financial analysis and investment, for example in the calculation of the Weighted Average Cost of Capital, in the Capital Asset Pricing Model and market-neutral …

In the previous post, we presented a system for trading VXX, a volatility Exchange Traded Note. The trading system was built based on simple moving averages.  In this post, we are going to examine the time series properties of VXX in more details. The figure below shows the VXX and …

Time series analysis is an important subject in finance. In this post, we are going to apply a time series technique to a financial time series and develop an investment strategy.  Specifically, we are going to use moving averages to trade volatility Exchange Traded Notes (ETN). Moving averages are used …

We have written many blog posts about the increase in volatility of volatility. See, for example Is Volatility of Volatility Increasing? What Caused the Increase in Volatility of Volatility? Similarly, last week Bloomberg reported, The sudden rise in volatility in February and March showed that even with strong growth fundamentals, …

The US equity market just reached new highs, and it broke many records.  For example, Bloomberg reported that the US market had not been overbought like this in 21 years. The S&P 500 Index’s superlative start to 2018 is making a contrarian technical indicator look silly. The benchmark gauge is …

Peter Carr recently gave a talk on volatility trading at the Fields institute. Summary: In general, an option’s fair value depends crucially on the volatility of its underlying asset. In a stochastic volatility (SV) setting, an at-the-money straddle can be dynamically traded to profit on average from the difference between …

The volatility index was created more than 30 years ago. Since then it has become a favorite tool for both speculation and risk management.  There is now strong evidence that VIX futures and related exchange-traded products are changing the market dynamics. Specifically, in the early days of the VIX, the …

Last Thursday witnessed, again, another dramatic increase in volatility. The volatility index VIX spiked 44 percent to 16.04%, its highest daily close for the year. As shown below, the VIX futures term structure inverted in the short end. Two days before the event, Helen Bartholomew of Reuters warned that the …