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I am trying to duplicate zero rates and discount factors from ql.PiecewiseLinearZero method. To simplify calculation, I only use one deposite rate: 3M Euribor 0.03822.

I set evaluationDate as ql.Date(11, 9, 2023) and I have only 2 nodes in the curve: ((Date(11,9,2023), 0.038036555682711436), (Date(13,12,2023), 0.038036555682711436)) which 0.038036555682711436 is the zero rates of the dates.

My question is: how to derieve the zero rate 0.038036555682711436 from Euribor 3M deposit rate 0.03822? I would be very grateful if anyone can help.

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    $\begingroup$ Do you know what a zero rate is? You use the equivalence relation: $1+dr_{3m} = e^{dr_{cc}}$ $\endgroup$
    – Attack68 ♦
    Commented Jun 9 at 16:11

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To expand a bit on @Attack68's comment: your input rate $r_s$ = 0.03822 is simply compounded, i.e., the notional plus interest after 3 months is $1 + r_s T$, with $T$ being 3 months. The curve you build, instead, happens to store the zero rates as continuously compounded rates, i.e., notional plus interest equals $e^{r_c T}$, hence the equivalence.

The exact value you'll get from solving the equation depends on calculating $T$ correctly. This involves a number of conventions such as the day count convention (probably act/360 since your deposit is based on Euribor), the calendar used for determining holidays (probably TARGET) and the convention to use to adjust holidays (Modified Following). It also depends, through the above, on the quotation date of the deposit and on the number of settlement days: if it's different from 0, the quoted rate is no longer a zero rate but a forward rate starting at a future settlement date.

Things get even more complex when you input swap rates into the curve. In general, calculating the nodes requires a root-finding process.

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  • $\begingroup$ thanks so much. I didn't realize 3M Euribor Deposit Rate was a forward rate before. $\endgroup$
    – Michelle
    Commented Jun 10 at 13:51

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