Python for Finance

Chapter 19. Volatility Options

We are facing extreme volatility.

— Carlos Ghosn

Volatility derivatives have become an important risk management and trading tool. While first-generation financial models for option pricing take volatility as just one of a number of input parameters, second-generation models and products consider volatility as an asset class of its own. For example, the VIX volatility index (cf. http://en.wikipedia.org/wiki/CBOE_Volatility_Index), introduced in 1993, has since 2003 been calculated as a weighted implied volatility measure of certain out-of-the-money put and call options with a constant maturity of 30 days on the S&P 500 index. Generally, the fixed 30-day maturity main index values can only be calculated by interpolating between a shorter and a longer maturity value for the index—i.e., between two subindices with varying maturity.

The VSTOXX volatility index—introduced in 2005 by Eurex, the derivatives exchange operated by Deutsche Börse AG in Germany (cf. http://www.eurexchange.com/advanced-services/)—is calculated similarly; however, it is based on implied volatilities from options on the EURO STOXX 50 index.^[81]

This chapter is about the use of the DX derivatives analytics library developed in Chapters 15 to 18 to value a portfolio of American put options on the VSTOXX volatility index. As of today, Eurex only offers futures contracts and European call and put options on the VSTOXX. There are no American options on the VSTOXX available on public markets. ...