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Rates conversion
Educational transforms between rate conventions. Start with continuous compounding — more blocks (forwards, …) later.
Continuous compounding
\(DF = e^{-z\,t}\) · C++
numeraire_cpp
Zero → discount
\[
DF = P(0,t) = e^{-z\,t}
\]
Discount → zero
\[
z = -\frac{\ln(DF)}{t},\quad t > 0
\]
Absolute rates (0.05 = 5%). Tenor \(t\) in years.
DF
0.95122942
round-trip z = 0.05000000
(input z = 0.05000000)
z Zero ·
DF Discount ·
t Tenor