In financial markets, the logarithms of asset prices are often modeled as a normal distribution. Elsewhere in life, many things are normally distributed: people’s height, education levels, talents, working hours in a day, etc. Success, as measured by wealth, however, is not normally distributed. In fact, it’s heavily skewed and follows the Pareto rule: 20%…
Read More Is It Better To Be Lucky Than Good?Portfolio hedging is a risk-management practice that uses a number of strategies to mitigate the risks of any given portfolio. Tail risk hedging in particular is one of the techniques used in equity portfolio management. It basically involves buying put options in a certain amount to partially or fully protect the portfolio. Reference [1] provided…
Read More Tail Risk Hedging Strategies: Are They Effective?Volatility estimators are a useful tool in volatility trading and risk management. We have discussed several types of volatility estimators, ranging from the simple Close-to-Close Historical Volatility to more complex ones like the Garman-Klass-Yang-Zhang volatility. As discussed in Reference [1], volatility estimators can also be used directly in delta-one trading by Commodity Trading Advisors. The…
Read More An Application of Volatility EstimatorsAccounting numbers are prevalent in financial reporting, business valuation, and investment management. They’re so frequently used that the practitioners rarely asked pragmatic questions such as: are they useful, do they account for some meaningful risks, can they be used to price assets. A recent article [1] attempts to bring some answers to these questions, This…
Read More Are Accounting Numbers Useful?Previously, we elaborated on why hedging is an important tool for risk management. We illustrated the importance of hedging with examples from the commodity, mortgage back securities, and foreign exchange markets. A recent paper [1] evaluated the hedging effectiveness of various range-based volatility estimators. Among them, we can find the commonly used GARCH model. Generalized…
Read More Hedging Market Risks Using Volatility Estimators-Are Sophisticated Methods Better?In a previous post, we presented theory and a practical example of calculating implied volatility for a given stock option. In this post, we are going to implement a model for forecasting the implied volatility. Specifically, we are going to use the Autoregressive Integrated Moving Average (ARIMA) model to forecast the volatility index, VIX. In…
Read More Forecasting Implied Volatility with ARIMA Model-Volatility Analysis in PythonIn a previous post, we presented an example of volatility analysis using Close-to-Close historical volatility. In this post, we are going to use the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model to forecast volatility. In econometrics, the autoregressive conditional heteroscedasticity (ARCH) model is a statistical model for time series data that describes the variance of the…
Read More Forecasting Volatility with GARCH Model-Volatility Analysis in PythonIn the previous post, we introduced the Garman-Klass volatility estimator that takes into account the high, low, open, and closing prices of a stock. In this installment, we present an extension of the Garman-Klass volatility estimator that also takes into consideration overnight jumps. Garman-Klass-Yang-Zhang (GKYZ) volatility estimator consists of using the returns of open, high,…
Read More Garman-Klass-Yang-Zhang Historical Volatility Calculation – Volatility Analysis in PythonIn the previous post, we introduced the Parkinson volatility estimator that takes into account the high and low prices of a stock. In this follow-up post, we present the Garman-Klass volatility estimator that uses not only the high and low but also the opening and closing prices. Garman-Klass (GK) volatility estimator consists of using the…
Read More Garman-Klass Volatility Calculation – Volatility Analysis in PythonIn 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 into account the information about…
Read More Parkinson Historical Volatility Calculation – Volatility Analysis in Python