Calibrating the solvency 2 standard formula

Discussion in 'SP9' started by Edwin, Mar 19, 2015.

  1. Edwin

    Edwin Member

    Hi all,

    I am busy with an exercise as part of building an Economic Capital model. Suppose I quantify my Lapse_risk to be 2000, and I use the implied assumption underlying the standard formula that this comes from a normal distribution. The 1 year VAR is;-

    \( \mu + \sigma \Phi ^ {-1}\left( \alpha \right)\) = 2000

    then it is impossible to get these parameters.

    However under the assumption of a zero mean (which I am still trying to see how it can apply to the Sep 2014 q6, as suggested by Simon James's last comment in this thread;- http://www.acted.co.uk/forums/showthread.php?t=10584

    I don't know why this will hold when the question asked for a 1 year VaR, also I thought the assumption of zero mean holds only when you can get positive and negative values in your series which doesn't seem to be the case in the question.

    But suppose someone convinces me then the 1 year VAR is;-

    NORMSINV(a)*\( \sigma \) = 2000, i.e 2.576*\( \sigma \) =2000, thus we have a \( N(\mu, \sigma) \) =N(0,776.39). Then I can do so many things with this information.
     
    Last edited by a moderator: Mar 19, 2015
  2. Viki2010

    Viki2010 Member

    The assumption of zero mean applies for short durations. For ST9 is 1 year considered still as short duration and anything above that would be long duration?

    It is quite subjective, but there is no clear cut rules it seems....
     
  3. Edwin

    Edwin Member

    Let's hear from Simon, but 1 YEAR is not short duration. In the markets when calculating the 1 DAY VaR that's when they assume zero mean since stock prices over 1 day should iid hence zero mean.
     
    Last edited by a moderator: Mar 19, 2015
  4. Edwin

    Edwin Member

    Simon, David, any help?
     
  5. Simon James

    Simon James ActEd Tutor Staff Member

    Hi - sorry for the delay in replying during the blocks.

    Assuming a zero mean is common for short periods in investment markets - by "short", I mean 1 or 10 days. Is 30 days a "short" period? Maybe?! It's a matter of judgement, company policy or regulator diktat.

    If I was looking at a year (say the 1-year VaR on a pension fund portfolio) I would expect to allow for a mean.

    Bear in mind the mean can simply just move the position from which you are measuring and you need to clear what you are looking for and how you are expressing the VaR.

    Let's say I have a portfolio worth 100 and there is a 5% chance that I will lose 20 and the value will fall to 80.

    • If I allow for growth over some period, the portfolio might be expected to grow to 105.
    • If there is still a 5% chance the value will fall to 80, then the VaR has increased to 25.
    • If there is still a 5% chance I will lose 20, the value of the portfolio may fall to 85 and the VaR is still 20.
     
  6. Edwin

    Edwin Member

    Thanks a lot Simon, but do you agree with my implied normality assumption?

    I need to convince someone about this.
     

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