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 …

For many of us, inflation has been a constant worry in recent years. One way to protect ourselves from the effects of inflation is by hedging our investments. So let’s take a look at how can we hedge against inflation. What is Inflation? Inflation is a type of rising in …

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 , volatility estimators can also be used directly in delta-one trading …

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 …