VaR
- Thread starter skoh
- Start date
Hi skoh, it's not a lot of context but it multiplies such that (normal relative) VaR = alpha*sigma[horizon "base"]*SQRT[horizon wanted/horizon "base"], so it's not so much VaR scaling as variance scaling linearly such that volatility scales by square root of time (under i.i.d.)
so scaling up from a 10-day volatility --> 1 year vol = 10-day "base" vol * SQRT [250 days wanted/10 days "base"] = 250 day volatility; relative VaR is just multiplies that by a deviate (confidence).
If you scale down from 1 year to 1-day, same rule: 1-day vol = 250-day vol * SQRT [1 days wanted/250 days "base"] ... but this is equal to 250-day vol / SQRT(250) = 1-day vol; so i'd expect you'd see the division only when scaling down to 1-day VaR/vol as SQRT(1) = 1.
it is easiest to assume, like Tuckman does, by convention that sigma is annual; e.g., 20% vol is 1-year volatility, then vol scales by *SQRT(dt) ... 10-day vol = 20%*SQRT(dt) where dt = 10/250; or, 3-year vol = 20%*SQRT(dt) where dt = 3 years
Thanks,
so scaling up from a 10-day volatility --> 1 year vol = 10-day "base" vol * SQRT [250 days wanted/10 days "base"] = 250 day volatility; relative VaR is just multiplies that by a deviate (confidence).
If you scale down from 1 year to 1-day, same rule: 1-day vol = 250-day vol * SQRT [1 days wanted/250 days "base"] ... but this is equal to 250-day vol / SQRT(250) = 1-day vol; so i'd expect you'd see the division only when scaling down to 1-day VaR/vol as SQRT(1) = 1.
it is easiest to assume, like Tuckman does, by convention that sigma is annual; e.g., 20% vol is 1-year volatility, then vol scales by *SQRT(dt) ... 10-day vol = 20%*SQRT(dt) where dt = 10/250; or, 3-year vol = 20%*SQRT(dt) where dt = 3 years
Thanks,
ABFRM
Member
it shud be calculated as σ√T. Var scales with the square root of time. extend one period VaR to T period VaR by multiplying by the square root of T. But there are two assumtions we are making here :
1) Random walk
2) Constant Volatility( which is not acceptable because it always change).
1) Random walk
2) Constant Volatility( which is not acceptable because it always change).
I agree Abhishek's assumptions are key, I've typically stated essentially the same assumptions as: the i.i.d. condition (also "finite variance" is a condition, but i omit it, b/c i think it's a bit esoteric).
Note "identical" distribution in i.i.d. is consistent with "constant volatility." Volatility is distributional 2nd moment; an identical distribution, by def, has constant variance.
I think i.i.d. ~= random walk--for working purposes, the same thing--although i'm under the impression that technically random walk is a superset (slightly more general case) of i.i.d. but i don't really know?
Note "identical" distribution in i.i.d. is consistent with "constant volatility." Volatility is distributional 2nd moment; an identical distribution, by def, has constant variance.
I think i.i.d. ~= random walk--for working purposes, the same thing--although i'm under the impression that technically random walk is a superset (slightly more general case) of i.i.d. but i don't really know?
Aleksander Hansen
Well-Known Member
A risk driver Y = ln(S t) can follow a random walk, yet not be i.i.d.
The transformation epsilon = ln(S t+1) - ln(St) will generally be i.i.d.
The transformation epsilon = ln(S t+1) - ln(St) will generally be i.i.d.
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