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# How to get a historical or theoretical volatility of index future

Discussion in 'Options' started by yip1997, Jun 28, 2006.

1. ### yip1997

Is there a way to compute the volatility of index future based on the underlying index?

Is there a website to find the historical volatility of index future?

2. ### MTE

You want historical volatility or historical implied volatility? If it is the former then just take the prices, stick them in excel and calculate standard deviation of daily log-returns. Then multiply by the square root of 252 to get annualised volatility.

3. ### yip1997

I want historical volatility of index future. Say for example, to compute s&p dec future volatility, you need a set of dec future price, but unlike the near-term future, they are not actively traded, and i don't think it gives you a good estimate of the volatility of the index future when it is close to expiration.

4. ### MTE

I don't see why you can't use the underlying index to calculate the volatility. The two are closely correlated anyway, true there's basis risk, but it's not that great.

5. ### yip1997

I think we can. I believe the index future volatility should be:

= sigma * exp(rt) based on the theoretical value of future price.

I just want someone to verify it.

6. ### alanm

Why do you think the futures have a different volatility than the index? I suppose, on a per-minute basis, they might, but any difference in the daily (or longer) volatility would only have to do with procedural/time differences in the way the closing prices are reported, or singular incidents that cause the FV calculation to change, like a huge, sudden interest rate move. Even then, there has to be a long time to expiration, and the move has to be truly huge to make any significant difference, and it will affect just that one day.

7. ### yip1997

First, I read a lot of academic books (e.g. Future, Options & Swaps from Robert Kolb) that Beta of index future is greater than 1.
Second, the fair future value is
F = S Exp(rt).

It seems that volatility of F should be related to the volatility of S by the same factor ( exp(rt) ). However, t decays as well. t decreases by 1 everyday.

So the upper bound of volatility of F = exp(rt) * volatility of S.

For small r, exp(rt) is close to 1, and so they are very close. However, with larger t and increasing interest rate, I like to get the exact formula, and I just wonder if anyone knows.

8. ### MTE

Why do you think the volatility of futures is related to volatility of spot by the same factor exp(rt)?

Volatility is calculated based on natural log returns, i.e. ln(S2/S1), so if we substitute S with F we get ln(S2*exp(rt)/S1*exp(rt-1)). So the difference between the spot volatility and futures volatility is that "one day" factor.

P.S. Why don't you just get a continuous contract price data and calculate your volatility from there!? Granted, it's not 100% accurate, but so what, historical volatility is just that historical volatility.

9. ### yip1997

MTE,

I never traded future, nor future options. I start looking into the possibility of trading future options b/c of higher leverage. My question might be very naive.

I just wonder how most traders switch from index option to future option, and how do they compute volatility.