How to Calculate Options Prices and Their Greeks: Exploring the Black Scholes Model from Delta to Vega

Chapter 3Volatility

Volatility is the measure of the variation (or the dispersion) of the returns (profits/losses) of a Future over a certain period of time.

One could say: the riskier the asset, the higher the volatility (think of market crashes). The lower an asset's risk, the lower its volatility (think of the summer lull). So, in highly volatile markets one could expect large moves of the Future where at low volatile markets there might be days where the Future hardly moves.

THE PROBABILITY DISTRIBUTION OF THE VALUE OF A FUTURE AFTER ONE YEAR OF TRADING

In option trading volatility is expressed on an annualised basis. It is a calculation of the daily returns based on a full year's expectation of the combined returns. The annualised volatility predicts the probability of the outcome of the value of a Future after one year of trading (usually 256 trading days).

The probability is based on the Gaussian distribution. With low volatility (for example, 10% as depicted in Chart 3.1), one could expect the Future, which initially started at 50, to settle somewhere between 40 and 60 after one year of trading. (Here a 95% confidence level has been applied, being 95% of all probable occurrences, and hence 2 standard deviations of 10%.) If the volatility is twice as high (20%), the range for the Future to settle after one year of trading would (almost) double as well, now between 30 and 70.

Chart 3.1 Probability distribution at 10% volatility

When volatility is at 40%, the range ...