In a previous post, we wrote about Employee Stock Options, a form of financial compensation that a company uses to reward its employees. In this post, we are going to discuss another form of compensation, Performance Share Units. Performance share units (PSUs) are hypothetical share units that are granted to …

Employee Stock Option (ESO) is a form of compensation that a company uses to reward, motivate, and retain its employees. An employee stock option (ESO) is a label that refers to compensation contracts between an employer and an employee that carries some characteristics of financial options. Employee stock options are …

In a previous post, we presented the binomial tree method for pricing American options. Recall that an American option is an option that can be exercised any time before maturity. A drawback of the binomial tree method is that the implementation of a more complex option payoff is difficult, especially …

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 …

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 …

Value at Risk (VaR) is a tool for measuring a portfolio’s risk. Value at risk (VaR) is a measure of the risk of loss for investments. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such …

Just like any financial derivatives that were initially designed for risk management purposes, interest rate swaps are an effective tool for managing and transferring interest rate risks as long as those risks are well understood.  But as banks and financial institutions are constantly trying to invent new financial products to …