Implied volatility
The implied volatility is a mathematical key figure for options and other derivative financial instruments with an option component. It can be interpreted as a measure of the fluctuation range currently expected on the market for the underlying asset over the remaining term of the option.
Differentiation from (historical) volatility
While the volatility (instantaneous standard deviation) is calculated from historical prices of the underlying asset , the implied volatility is determined from current option prices. If the price of an option and the factors influencing the price of the term, price of the underlying asset, interest rates and exercise price are known, the implied volatility can be derived from these values using an option price model .
The formula of the Black-Scholes model and the other common option price models cannot be converted explicitly according to the volatility. Numerical approximation methods must be used for the calculation. In the case of European standard options, which are described by the Black-Scholes model, the Newton-Raphson method can be used . It is very efficient and, for typical desired accuracies, converges to the implied volatility sought after within three or four iterations.
Market behavior
When share prices rise, the implied volatilities usually fall and vice versa. The closer "in the money" a purchase option , the lower their implied volatility (at put options other way around). If you plot the implied volatility on a y-axis and the exercise price of the option on the x-axis, you get a graph called the volatility smile .
Volatility indices
The volatility indices VDAX and VDAX-NEW calculated by Deutsche Börse reflect the implied volatilities of standard options on the DAX with remaining terms of 45 and 30 days respectively. For the Swiss stock market there are the volatility indices VSMI and VLEU , for the S&P 500 it is the VIX and the Dow Jones Euro Stoxx 50 includes the VSTOXX .
Since the implied volatility is comparatively high in turbulent stock market phases, volatility indices are often referred to colloquially as "fear barometers".
The volatility indices are usually in the state of contango . The longer terms are usually more expensive than the shorter ones. If you sell volatility, you will usually get rolling profits, which is why selling volatility has become a popular strategy.
The Volax Future introduced in 1998 on the implied volatility of a DAX option “at the money” with a remaining term of three months was discontinued in the same year due to the sharp drop in liquidity.
literature
- Andreas Dartsch: Implied volatilities on the stock and options market. Deutscher Universitätsverlag et al., Wiesbaden 1999, ISBN 3-8244-6926-X ( Gabler Edition Wissenschaft ), (also: Duisburg, Univ., Diss., 1998).
Web links
Individual evidence
- ↑ Guide to the volatility indices of Deutsche Börse. Version 2.4. (PDF; 163 kB) Deutsche Börse AG, January 2007, archived from the original on November 22, 2009 ; Retrieved November 4, 2009 .