Hi,I'm a bit confused on how to convert a garch of log returns into a dollar value. My understanding is that garch will give us the volatility. The square root of that is the standard deviation. But just multiplying the SD times the price does not appear to produce the correct values. (They seem too large.)To make is simpler, if I have 100 prices and first calculate the log returns:then calculate the volatility:I have the volatility of the log returns. How can I convert that back to a physical dollar value. I want to answer the question, "How many dollars/cents is one standard deviation given the current price and volatility of returns."Thanks!

This is not a GARCH process. In your example, you are computing historical vol.Just like you said, the volatility is the square root of variance. Keep in mind this is the daily vol, assuming you are using daily prices. To annualize it, multiply the variance by 252 trading days in a year.The volatility of log returns is the geometric standard deviation. One standard deviation about the current price is and one below is .

Hi,My example is about understanding the relationship between log of returns and dollar values. (I didn't write out all the math for GARCH here as that isn't very relevant to the question.)My understanding of GARCH is that, if reasonably accurate, is one way to estimate volatility. Historical returns are another. I've seen many comparisons between the two. Ultimately, we're looking at the volatility. Thanks!

There isn't really a dollar value for standard deviation of log returns because it is a multiplicative factor. You could use the arithmetic standard deviation of the lognormal distribution.Your dollar volatility would be: