So, if I want to calculate the EPV of a 3 year annuity due, with
q0 = .01, q2 = .02, and q3 = .04, and i = .05, I recently discovered that it can be calculated two 'different' ways.
In the one case, you let X be the occurrence that exactly that number of payments were made, and its associated probabilty, and in the other case, you look at the chances of a particular future payment being made.
so, a double dot = 1(.01) + (1 +1/1.05)*.99*.02 + (1+1/1.05+1/1.05^2) *.99*.98 = 2.82268
Or, alternatively, and perhaps more intuitively
a double dot = 1 +1/1.05*.99+1/1.05^2*.99*.98 = 2.82268
(Last way seems easier...)
but, what if I want to calculate the Variance.. I can use the first formula to calculate E(x^2) = 1^2(.01) + (1 +1/1.05)^2*.99*.02 + (1+1/1.05+1/1.05^2)^2 *.99*.98 = 8.01805 .. Leads to the variance of 8.01-2.82^2 = .04957
Is there an existing formula/ trick I could have used to calculate the variance given that I have already calculated the EPV of the annuity? (and thus can calculate the EPV the second way, which is fastest.)
q0 = .01, q2 = .02, and q3 = .04, and i = .05, I recently discovered that it can be calculated two 'different' ways.
In the one case, you let X be the occurrence that exactly that number of payments were made, and its associated probabilty, and in the other case, you look at the chances of a particular future payment being made.
so, a double dot = 1(.01) + (1 +1/1.05)*.99*.02 + (1+1/1.05+1/1.05^2) *.99*.98 = 2.82268
Or, alternatively, and perhaps more intuitively
a double dot = 1 +1/1.05*.99+1/1.05^2*.99*.98 = 2.82268
(Last way seems easier...)
but, what if I want to calculate the Variance.. I can use the first formula to calculate E(x^2) = 1^2(.01) + (1 +1/1.05)^2*.99*.02 + (1+1/1.05+1/1.05^2)^2 *.99*.98 = 8.01805 .. Leads to the variance of 8.01-2.82^2 = .04957
Is there an existing formula/ trick I could have used to calculate the variance given that I have already calculated the EPV of the annuity? (and thus can calculate the EPV the second way, which is fastest.)
Annuities Due
