[R-SIG-Finance] [R-SIG-Fin​ance] convert volatility of log returns to dollars

[Arun Kumar Saha]

Dear Noah, first of all I would not suggest to do any statistical
calculation directly on price as price generally non-stationary, hence
you might get spurious result. Therefore may be your analysis like:

mean(x)
758.9125

sd(x)
2.61521

may be incorrect.

Now coming to your main question, if I understood your problem
correctly, then your are perhaps asking: how to calculate dollar
volatility.

To answer this, I would rather go for some ***model based realism***
hence would assume following simple model as DGP for price:

log(y[t+1]) = log(y[t]) + epsilon[t+1], epsilon[t+1]~N(0, 0.001201941^2)

Therefore given y[t], you can easily estimate the SD of y[t+1], using
some simple arithmetic of log-normal distribution.

However there is some approximate approach as well...........

y[t+1]) -y[t] = y[t] * (y[t+1]) -y[t])/y[t] = (approximately) y[t] *
log(y[t+1]/y[t]) = y[t] * epsilon[t+1]

Therefore given y[t], you can again easily estimate the SD of y[t+1]),
which will be your dollar volatility.

HTH
_____________________________________________________

Arun Kumar Saha, FRM
QUANTITATIVE RISK AND HEDGE CONSULTING SPECIALIST
Visit me at: http://in.linkedin.com/in/ArunFRM