## Tutorials and Reference

Below you can find VIX futures and options expiration calendar for 2020 and 2021, as well as full VIX expiration dates history (2004-2019) 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…]

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 differences between types of volatility – implied, realized, historical. There are other types and terms which we will also explain, including forecast volatility, future volatility, and statistical volatility. How They Differ Volatility, typically expressed as a percentage and interpreted as standard deviation of returns, measures how [more…]

The objective of this page is to explain 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 VIX, you may first want to [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…]

Higher order Greeks are option Greeks other than first order Greeks (first order Greeks include delta, theta, vega, and rho). They measure sensitivity of first order Greeks to factors like underlying price, volatility, time, or interest rate, in a similar way that first order Greeks measure sensitivity of option price [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…]

This page explains differences between American and European options and their prices. We will also discuss the origin of these terms, which most sources don’t mention. Main Difference: When They Can Be Exercised European options can be exercised only at expiration. American options can be exercised at any time from [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 detailed guide to calculating historical volatility 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, including Yahoo Finance or Google Finance [more…]

This page is a detailed guide to finding and downloading historical data such as daily stock prices or index values from Yahoo Finance. Go to Yahoo Finance homepage: finance.yahoo.com At the moment and on my computer it looks like this. It may look a little different on your device, but [more…]

Put-call parity is a relationship between prices of European call and put options (with same strike, expiration, and underlying). It is defined as C + PV(K) = P + S, where C and P are option prices, S is underlying price, and PV(K) is present value of strike. This page [more…]