QuantLib Discounting: Continuous Versus Annual Compounding
Summary
This note explains why a one-year cash flow discounted with QuantLib’s FlatForward curve may not produce the value expected from a nominal annual rate. The key is the curve’s default compounding convention: the rate is treated as continuously compounded, so discounting a payment of 110 over one year at 10% gives about 99.53 rather than 100. Specifying annual compounding yields the expected present value in the example.
The example uses CashFlows.npv with a zero payment on the evaluation date and a later payment, and compares Actual/365 and 30/360 day-count conventions. The reported discrepancy is attributed to compounding, not those day-count choices. This is a focused QuantLib usage explanation; it does not cover other curve settings, cash-flow schedules, or the broader valuation effects of compounding conventions.
Key ideas
- QuantLib’s FlatForward curve uses continuous compounding by default.
- Continuous compounding at 10% discounts a one-year payment of 110 to about 99.53.
- Annual compounding produces a present value of 100 in the example.
- Day-count conventions alone do not explain the reported difference.
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Full text
# QuantLib Python: why is the NPV different? NPV(0.1,[0,110]) should be 100, not 99.53
# QuantLib Python: why is the NPV different? NPV(0.1,[0,110]) should be 100, not 99.53
I am trying to learn QuantLib for Python. Further to my previous question on the syntax for CashFlows.npv(), now that I understand how the syntax works, I have a question on why the output differs from what I'd expect (which is why I think a separate question is justified).
In my toy example, my cashflows are zero on 15-Jan-2001 and 110 on 15-Jan-2002. If I discount them at 10%, I'd expect the pv to be 100, but I get 99.53211. Why? What am I missing? That would imply that 384 days have gone by, not 365. Those are not leap years. I have tried with act/365 and 30/360: they both give the same result, which is not 100.
```
import QuantLib as ql
d1 = ql.Date(15,1,2001)
ql.Settings.instance().setEvaluationDate(d1)
cfs = [ql.SimpleCashFlow(0, d1),
ql.SimpleCashFlow(110, d1 + 365)]
calc_date = d1
risk_free_rate = 0.1
curve_act_365 = ql.YieldTermStructureHandle(
ql.FlatForward(calc_date, risk_free_rate, ql.Actual365Fixed()))
pv_act_365 = ql.CashFlows.npv(cfs, curve_act_365, True)
curve_30_360 = ql.YieldTermStructureHandle(
ql.FlatForward(calc_date, risk_free_rate, ql.Thirty360()))
pv_30_360 = ql.CashFlows.npv(cfs, curve_30_360, True)
```
## Answer by David Duarte (score 6, accepted)
https://quant.stackexchange.com/a/61006
By default, QuantLib expects a continuously compounded rate in the FlatForward constructor.
So the PV you are getting is basically:
```
from math import exp
print(110 * exp(-0.1))
```
If you define your curve with an annually compounded rate like so:
```
curve_30_360 = ql.YieldTermStructureHandle(
ql.FlatForward(calc_date, risk_free_rate, ql.Thirty360(), ql.Compounded, ql.Annual))
```
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.