## Tutorials and Reference

Below you can find options expiration calendar for 2021 and 2022 for standard US traded monthly and weekly equity, equity index, and ETF/ETN options. For VIX options and futures, see VIX Expiration Calendar. 2021 Monthly options expirations: 15 January 2021 19 February 2021 19 March 2021 16 April 2021 21 [more…]

Below you can find VIX futures and options expiration calendar for 2021 and 2022, as well as full VIX expiration dates history (2004-2020) and explanation of VIX expiration rules. For standard US equity, index and ETF options (including options on VIX ETFs and ETNs) see: Standard US Equity and Index [more…]

VIX Futures Curve Explained A futures curve is a curve made by connecting prices of futures contracts of the same underlying, but different expiration dates. It is displayed on a chart where the X-axis represents expiration dates of futures contracts and the Y-axis represents prices. The chart looks quite similar [more…]

In option pricing, volatility modeling, and quantitative finance in general, you often need the number of trading days per year as a parameter for your model. Which number to choose? Trading Days per Year in US Markets How many trading days per year are there in the US stock and [more…]

This page explains the Black-Scholes formulas for d1, d2, call option price, put option price, and formulas for the most common option Greeks (delta, gamma, theta, vega, and rho). Black-Scholes Inputs According to the Black-Scholes option pricing model (its Merton’s extension that accounts for dividends), there are six parameters which [more…]

This page explains the logic of VIX calculation and some of the underlying assumptions and parameters. Exact formulas are available in a short pdf named VIX White Paper on the official website of CBOE. If you are not familiar with the VIX index, you may first want to see a [more…]

This page is a detailed guide how to calculate Relative Strength Index (RSI). You can see how the formulas work in Excel in the RSI Excel Calculator. The calculation is explained in detail in chapter 4 of the calculator’s guide. RSI Calculation Formula RSI = 100 – 100 / ( 1 [more…]

This page shows how to convert implied volatility (typically annual standard deviation of returns) to daily volatility and how to interpret it in terms of expected daily price changes with given probabilities. Note that in the Implied Volatility Calculator you don’t need to do the conversion, as the calculated implied [more…]

This page is a guide to creating your own option pricing Excel spreadsheet, in line with the Black-Scholes model (extended for dividends by Merton). Here you can get a ready-made Black-Scholes Excel calculator with charts and additional features such as parameter calculations and simulations. Black-Scholes in Excel: The Big Picture [more…]

This is the second part of the Black-Scholes Excel guide covering Excel calculations of option Greeks (delta, gamma, theta, vega, and rho) under the Black-Scholes model. Calculating Black-Scholes Greeks in Excel I will continue in the example from the first part to demonstrate the exact Excel formulas. See the first [more…]

This page is an overview of main events and papers related to the Black-Scholes option pricing model. Besides works of its main authors, Black, Scholes, and Merton, we will also investigate earlier ideas which influenced the model, and other researchers (many of them famous for other models) who played a [more…]

Strike price (also called exercise price) is the price at which you can buy the underlying security when exercising a call option, or the price at which you can sell the underlying when exercising a put option. Spot price means the current market price. In short: spot price = now, [more…]

This is a detailed guide to calculating Average True Range (ATR) in Excel. We will first calculate true range and then ATR as moving average of true range. We will do all the three popular ATR calculation methods – simple, exponential, and the original Wilder’s smoothing method. You don’t need [more…]

This page is a step-by-step guide to calculating variance and standard deviation. You can easily calculate variance and standard deviation, as well as skewness, kurtosis, percentiles, and other measures, using the Descriptive Statistics Excel Calculator. Definition of Variance Variance is a measure of dispersion in a data set. It measures [more…]

This is part 4 of the Option Payoff Excel Tutorial. In the previous parts (first, second, third) we have created a spreadsheet that calculates profit or loss for a single call or put option, given the strike price, initial option price and underlying price. Now we are going to expand [more…]

This is part 5 of the Option Payoff Excel Tutorial, which will demonstrate how to draw an option strategy payoff diagram in Excel. In the previous four parts we have explained option profit or loss calculations and created a spreadsheet that calculates aggregate P/L for option strategies involving up to [more…]

This is part 6 of the Option Payoff Excel Tutorial. In the previous parts we have created a spreadsheet that calculates profit or loss for option strategies and shows the payoff diagram. Now we are going to calculate maximum possible loss (risk) and maximum possible profit. You can often get [more…]

This is part 7 of the Option Payoff Excel Tutorial. In the previous part we have learned about useful properties of the payoff function and calculated maximum possible profit and maximum possible loss for an option strategy with up to four legs. In this part we will use the results [more…]

This is part 8 of the Option Payoff Excel Tutorial. In the previous parts we have created a spreadsheet that calculates P/L of an option strategy, draws payoff diagrams and calculates maximum profit, maximum loss and risk-reward ratio. In this section we will calculate break-even points – the exact underlying [more…]

This page explains how to calculate historical (realized) volatility from daily closing prices in Excel. Things Needed for Calculating HV in Excel Historical data (daily closing prices of your stock or index) – there are many places on the internet where you can get it for free, such as Yahoo [more…]