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Recently, the German government issued a long-dated bond with a 0% coupon.

I'm trying to implement a historical VaR model and would like to know the best way to model the historical returns of this bond.

What's tripping me up is the possibility that the return series could be "corrupted" due to:

a) the low level of rates

b) the possibility of having 0% in the denominator

Let's assume the returns are:

t_0 = 0% YTM

t_1 = 0.01% YTM

t_2 = 0.025% YTM

t_3 = 0% YTM

t_4 = -0.01% YTM

t_5 = 0% YTM

t_6 = 0.03% YTM

What's the best way to model these returns?

Thanks!

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  • 3
    $\begingroup$ Why does a zero coupon bond create any mathematical difficulties? The price is $P=100/(1+ytm)^N$. $\endgroup$ – Alex C Oct 10 at 16:05

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