Bugs item #2691902, was opened at 2009-03-18 15:28
Message generated for change (Tracker Item Submitted) made by klriedel
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Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Karl Riedel (klriedel)
Assigned to: Nobody/Anonymous (nobody)
Summary: Bootstrapping for bonds: Inconsistency in the clean price
Initial Comment:
Dear ladies and gentlemen,
when considering the bootstrapping of a coupon bond according to the example "FittedBondCurve.cpp" I found an inconsistency in the results of the bootstrapper according to
boost::shared_ptr<YieldTermStructure> ts0 (
new PiecewiseYieldCurve<Discount,LogLinear>(curveSettlementDays,
calendar,
instrumentsB,
bondDayCount));
This inconsistency was as follows: For simplicity I considered a coupon bond with only one remaining payment date t_1, at which the coupon c and the redemption 1 will be paid. Let t_0 be the last coupon date and today t is within the interval [t_0,t_1]. For this situation the discount factor df(t,t_1) was calculated according to
Clean Price = df(t,t_1) * [ 1 + c*(t_1-t) ]. (1)
This formula refers to a Clean Price which is theoretically correct, i.e. the accrued amount is discounted.
On the other hand, what has actually to be paid (marked standard) for a bond is the Clean price + the accrued amount according to the simple formula c*(t-t_0) which does not take into account discounting the accrued amount. The net present value of future payments must equal the spot price:
Clean Price + c * (t-t_0) = df(t,t_1) * [1+c]. (2)
In the middle of a payment period the resulting discount factors df(t,t_1) of (1) and (2) differ most. In my example this lead to a difference in the zero rate of around 10 BIPs.
Best regards,
Karl Riedel
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