Estimating Volatility VI
There are 157 five-day intervals between January 1, 1999, and August 18, 1999. Here is the histogram of the 157 five-day percentage changes in IBM from January 1999 to August 18:
Estimating Volatility V
Using this histogram, which is a picture of the historical data back to the beginning of this year, you can estimate, for instance, the chance that a one-day percentage change will be greater than 2%, or less than -1%, as follows:
Compuing Five Day Volatility
Suppose you are looking at an IBM option with five trading days to expiration. How much variation can you expect to see in the next five days?
Estimating Volatility III
In Tuesday’s (8/24/99) commentary we saw that option values vary quite a lot depending upon which volatility figure you use.
Estimating Volatility II
In the last commentary, we saw that when you compute the volatility of IBM over various look-back periods, you get the various one-day volatility values.
Estimating Volatility
As I have pointed out several times in these commentaries, the volatility that counts in determining the current value of an option, put or call, is the future volatility between now and expiration of the option.
Robustness of Volatility
Last Thursday we looked at a stock with historical annualized 100-day volatility of 60%, selling $100, with a September call with strike price 100 selling for $4.50, and saw that normal interest rate variation did not make a lot of difference in the call value.
Gamma
In the second of several articles, Bob Pisani explains how gamma, one of the option “Greeks,” can help you better understand the dynamics of your option positions.
Robustness
Suppose you believe a stock has a historical annualized 100-day volatility of 60%, that the stock is selling now for $100, a September 100 call on the stock is selling for $4.50, and you compute the value of the call to see if it is overpriced or underpriced.
Volatility: Theory vs. Reality
This information will tell you if the model prices overestimate, underestimate or properly estimate the true values of the underlying’s options.
A Closer Look At Volatility
In previous commentaries I’ve discussed how volatility varies depending on the time interval over which it is measured–namely, it increases with the square root of the time interval.
Volatility Revisited
I have gotten a number of questions about volatility and I’d like to offer a little more insight about this important subject.