Stochastic Interest Rate Models - Variance property doubt.

Discussion in 'CT1' started by playful27, Apr 15, 2014.

  1. playful27

    playful27 Member

    One of the properties of variance is that, var(1+\(i_{t}\)) = var(\(i_{t}\))
    I've done the StatsPack a year ago and therefore my stats is a bit rusty. Can anyone help me with this?
     
  2. cjno1

    cjno1 Member

    The variance of the sum of independent random variables is just the sum of the variances i.e. Var(X + Y + Z) = Var(X) + Var(Y) + Var(Z) as long as X, Y and Z are independent.

    1 and i_t are independent, since it doesn't matter what i_t is, 1 will always be 1!

    So

    Var(1 + i_t) = Var(1) + Var(i_t)

    The variance of a number is 0, since the value is always the same, so this just equals Var(i_t)
     
  3. playful27

    playful27 Member

    That was a quick response, and a very good one too!

    Thank you so much. You've explained it very clearly! :)

    Cheers.
     

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