October 29th, 2006, 2:47 pm
There are lots of volatilities in finance. For a stock price, one usually measures the standarddeviation of a logarithmic return series { log[S(t)/S(t-1)] }. These standard deviations vary because ofsampling error and because whatever causes volatility (news of the day) itself varies in intensity.The latter effect is called the volatility of volatility. (I attach a chart from a book of mine on this general subject).Black and Scholes invented an option pricing model where volatility is a (constant) parameter.You can report option prices by calculating what constant works: this is called the implied volatility.If you do this over time, you see the putative constant in fact varies: this is anothermanifestion of the volatility of volatility. To improve the model, one can use stochastic volatility, whichis a stochastic process for volatility, with a term representing the vol of vol.Use the forum search button for more discussion. You could also go the cboe.com and look at their VIX series.regards,
Last edited by
Alan on October 28th, 2006, 10:00 pm, edited 1 time in total.