what is the difference between conditional and unconditional volatility?
thanks in advance
Dear Srikanth
Unconditional volatility is the variance of the returns (r):
var (r) = E(r - E(r))^2
Whereas conditional volatility is the conditional variance, and conditional variance is the variance of returns given a model with information (M):
cond var (r) = E(r - E(r) I M))^2
In finance I am using returns (r), however, the variable can represent other things such as frequency, weight, concentration, et cetera.
It depends on how conditional volatility is defined.
In the GARCH literature, volatility
(1) V(Yt+1 | Φt)
is conditioned on past information represented by Φt.
In this case, the unconditional volatility is given by
(2) V(Yt+1) = E(V(Yt+1 | Φt) ).
Consider the simplest GARCH form
(3) Vt+1 = a + b * et^2 + c * Vt,
where E(et^2) = V and E(Vt) = V; the latter imply that Yt has stationary variance. Then, the unconditional variance can be obtained from (3) by taking unconditional expectations on both sides of the equation, i.e.,
E(Vt+1) = V = a + b * E(et^2) + c * E(Vt)
= a + b * V + c * V,
thus
(4) V = a / (1 - b - c).
In general,
(5) V = V(Y) = E(V(Y | X)) = E(E(Y^2 | X)) - E(E(Y | X))^2,
where X is another random variable. This equation can be applied to segmented regression models.
Srikanth.. Cox has replied your query however unconditional volatility is variance of returns while conditional volatility is conditional upon an information set... let me elaborate volatility calculated using any GARCH family techniques are example for reference check chris brooks on financial ecometrics
Going by Raymond’s definition,
var(r | M)
is the variance of returns based on M, which may be anything, e.g., knowledge of past data, beliefs of forecaster, stock splits, merger, firing of the company’s CEO etc.
Yes is the short answer. M (the information model) should be sophisticated such that it specifies the distribution (outcomes with probabilities) which can vary (or be different) contingent on stated events.
The difference is clear. While the unconditional variance is just the standard measure of the variance, the conditional variance represents the measure of the uncertainty about a variable given a model and an information set .
Explanation assuming a process like shared by Panayiotis Theodossiou has much clear insight.
Conditional volatility is the volatility of a random variable given some extra information. In the GARCH model, the conditional volatility is conditioned on past values of itself and of model errors. Unconditional volatility is the general volatility of a random variable when there is no extra information.
Unconditional variance (Variance) = Mean of the conditional variances + variance of the conditional means
Unconditional volatility can be seen as the volatility of a random variable while Realized volatility is the empirical unconditional variance over a given time period.
Conditional volatility is the volatility of a random variable given some extra information. In the GARCH model, the conditional volatility is conditioned on past values of itself and of model errors. Unconditional volatility is the general volatility of a random variable when there is no extra information.
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