Accounting 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 attempts to bring some …

Inflation refers to the decrease in a currency’s purchasing power. It can come as a result of various factors. Inflation isn’t necessarily a bad thing, as it can also accompany positive changes. However, it usually has adverse effects on businesses and individuals. Inflation risk, also known as purchasing power risk, …

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 evaluated the hedging effectiveness of various range-based volatility estimators. Among them, we can find the …

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 …

In 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 …

How do you determine the volatility of an unlisted entity, and more generally, how do you forecast volatility? These are non-trivial questions. There is an interesting discussion on Stackexchange: Here is a question I had for a long time but I never asked. Let’s take an easy example, AirBnb will …

In 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 …

In 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 …

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 …