Re: [Quantlib-users] Yield calculation - derivative for Newton method

[Lukasz S. <luk...@su...>]

Hi Francois,

Thank you for the quick reply. I guess my problem is simpler that you 
assumed.

I'm just using the BondFunctions function 'yield' with a constant yield 
(a single

number / rate; not a non-trivial forward curve).

So, my question is just if the Newton procedure for finding yield of a bond

gets correct inputs, because I ran into problems when trying to simply 
replicate

the formulas I seem to find in the C++ QuantLib source code available in the

web - the npv derivative seems to be modifiedDuration there, without

multiplication of the result by npv, which seems wrong. But I may be

mistaken.

Best regards,

Łukasz




On 8.05.2023 11:47, Francois Botha wrote:
>
> *Warning: This message originated from outside the organization. Use 
> caution when following links or opening attachments.*
>
> Hi Lukasz,
>
> Just to note that QLNet is an independent C# port of Quantlib (the C++ 
> version).
>
> That said, I'm guessing you're bootstrapping either on Zero or 
> Forwards rates and the default implementations of these have rates set 
> to a maximum of 300% ( 
> https://github.com/amaggiulli/QLNet/blob/d3b709a76098d5765b11da83d0217786b118bd58/src/QLNet/Termstructures/Yield/Bootstraptraits.cs#L100 
> and 
> https://github.com/amaggiulli/QLNet/blob/d3b709a76098d5765b11da83d0217786b118bd58/src/QLNet/Termstructures/Yield/Bootstraptraits.cs#L179).
>
> The implementation in Quantlib original is similar. I just briefly 
> glanced at the code and saw some branching related to the 
> QL_NEGATIVE_RATES preprocessor directive, which might be relevant. Try 
> enabling that directive. If that fails, you can implement your own 
> class that implements ITraits<YieldTermStructure> but removes the 300% 
> cap. I've had to use a variation of the last solution, but with my own 
> constraints, which in the end worked for me.
>
> Maybe someone else here has better suggestions.
>
> regards
> Francois Botha
>
>
> On Mon, 8 May 2023 at 11:10, Lukasz Skowronek 
> <luk...@su...> wrote:
>
>     Hi,
>
>     My name is Lukasz and I'm currently working on a small summary
>     screen for various bonds
>
>     that uses QuantLib under the hood.
>
>     I got an error report from our testers for the following inputs:
>
>     request.CouponPaymentsPerYear=1;
>     request.Coupon=0.0;
>     request.RedemptionPrice=100.0;
>     request.CleanPrice=1376.0;
>     request.FaceValue=1000.0;
>
>     ...
>
>     request.ExpirationDate=newDateTime(2024, 6, 27);
>     request.InvestmentDate=newDateTime(2023, 2, 9);
>
>     In short, this input corresponds to a zero coupon bond priced
>     extremely high (at 1376%).
>
>     The error I'm getting says the solver cannot bracket the root of
>     the target function.
>
>     After shifting the dot in the clean price by one decimal place, I
>     get the code to work
>
>     as expected. Still, even if the testers did not intend to
>     challenge my code with
>
>     bonds priced at a 85% markup (that is, -85% yield), I would expect
>     the solver to
>
>     find the root for the original input.
>
>     Digging into QuantLib's source code, I traced a few pieces related
>     to how yield
>
>     calculation is really done:
>
>     In *bondfunctions.cpp (line 360):*
>
>     Rate BondFunctions::yield(const Bond& bond, ...
>
>     in *bondfunctions.hpp (line 160):*
>
>     static Rate yield(const Solver& solver, ...
>
>     in *cashflows.hpp (line 276):*
>
>     static Rate yield(const Solver& solver, ...
>
>                 IrrFinder objFunction(leg, npv, dayCounter, compounding,
>                                       frequency,
>     includeSettlementDateFlows,
>                                       settlementDate, npvDate);
>                 return solver.solve(objFunction, accuracy, guess,
>     guess/10.0);
>
>     and finally, in *cashflows.cpp (line 728):*
>
>     CashFlows::IrrFinder::IrrFinder(const Leg& leg, ...
>
>         Real CashFlows::IrrFinder::operator()(Rate y) const {
>             InterestRate yield(y, dayCounter_, compounding_, frequency_);
>             Real *NPV = CashFlows::npv(leg_, yield,**
>     **includeSettlementDateFlows_,**
>     **                                  settlementDate_, npvDate_);*
>             return *npv_ - NPV*;
>         }
>
>         Real CashFlows::IrrFinder::derivative(Rate y) const {
>             InterestRate yield(y, dayCounter_, compounding_, frequency_);
>             return *modifiedDuration(leg_, yield,**
>     **includeSettlementDateFlows_,**
>     **                                settlementDate_, npvDate_)*;
>         }
>
>     Is this target function + derivative correct?
>
>     What worked on my side, when simulating the Newton method for
>     finding the root
>
>     separately, was:
>
>     doublef(doublerate) {
>     InterestRateir=newInterestRate(rate, dayCounter,
>     Compounding.Compounded, frequency);
>     return(cleanPrice+bond.accruedAmount(investmentDate))
>     *bond.notional(investmentDate) /100.0-
>     CashFlows.npv(bond.cashflows(), ir, false, investmentDate,
>     investmentDate);
>     }
>     // <-- target function
>     doubled(doublerate) {
>     InterestRateir=newInterestRate(rate, dayCounter,
>     Compounding.Compounded, frequency);
>     returnCashFlows.modifiedDuration(bond.cashflows(), ir, false,
>     investmentDate, investmentDate) *CashFlows.npv(bond.cashflows(),
>     ir, false, investmentDate, investmentDate);
>     }
>     // <-- derivative
>     (this is C# code that has QLNet as dependency)
>
>     Hence, there is an additional multiplication by CashFlows.npv(...,
>     which plays well with the
>
>     definition of modified duration as -dPdy / P
>
>     There does not seem to be a similar factor in QuantLib.
>
>     Am I mistaken? Is the multiplication by NPV in the derivative
>     handled some other way?
>
>     Best regards,
>
>     Lukasz Skowronek
>
>
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