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felix123321
Topic Author
Posts: 2
Joined: June 17th, 2020, 11:02 am

### Parametric Value at risk for savings plan

Hi all!

I have a question on how to calculate the parametric 95% VaR for a savings plan that is investing in a risky asset.
We have an initial amount and in addition monthly recurring investments.
Without monthly payments the answer is easy (Standard delta norm. dist. VaR):

Var = ((1+r)^t - 1,65*v*(t)^0,5) * x

x = Initial investment
v = Expected (monthly) volatility of asset
r = Expected (monthly) return of asset
t = Total period in months

How is that calculated with regular payments (of equal size).
I have not found any closed end parametric solution for this problem so far and run out of time : (
I am thankful for any indication or link to a solution.

Best regards,
Felix

Alan
Posts: 10497
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### Re: Parametric Value at risk for savings plan

I will guess there is no closed form -- as it looks like you need the distribution of a sum of correlated lognormal variates. My advice is to just spend a day and develop a nice Monte Carlo with errors below your required accuracy. It will run in a few seconds and then you'll be done.

felix123321
Topic Author
Posts: 2
Joined: June 17th, 2020, 11:02 am

### Re: Parametric Value at risk for savings plan

ok understood .. that would be the alternative

DavidJN
Posts: 1770
Joined: July 14th, 2002, 3:00 am

### Re: Parametric Value at risk for savings plan

Wasn't the usual solution strategy for parametric VaR to map the portfolio cash flows to standardized tenors that one can find a covariance matrix for? This was explained with examples in the original Riskmetrics technical documentation.

Alan
Posts: 10497
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### Re: Parametric Value at risk for savings plan

Sounds like an approximation worth exploring.

Another approach -- likely related -- would be to look at approximate Asian option valuation (w/ monthly averaging). You could split the terminal distribution into the sum of two correlated variates: one from the initial investment and a second from the sum of the (presumably equal) monthly investments. The terminal distribution of the latter can perhaps be well-approximated by the Asian option arguments.

The advantage of first developing an accurate Monte Carlo is that, once you have it, you can then go on to test approximations.

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