Re: [Quantlib-users] Inconsistency in ZSpread calculation?

[Peter C. <pca...@gm...>]

Hi Jian, this might be due to

- different compounding conventions for the spread in the z-spread
calculation (compounded in your code) vs. the zero-spreaded term
structure (defaults to continuous, you can change it but I am not sure
if this is this possible in Python)

- different day count conventions for the z-spread (given by day_count
in your code) and for the spread in the zero-spreaded term structure,
which is always the day counter of the underlying rate curve (your
ts_handle) - again you can overwrite this in the zero-spreaded term
structure constructor, but this is unfortunately ignored (a known bug,
or an open to do as we often like to call it)

Best regards,
Peter

On Sun, 22 Nov 2020 at 19:00, jian Xu <jia...@gm...> wrote:
>
> Hi,
> I encountered some inconsistency in ZSpread calculation.  Basically, I
> calculate the zspread using the BondFunctions.zSpread.  But when I add
> this zspread on top of the yield curve, I cannot recover the clean
> price.  Following is what I did:
>
> I used the official notebook example at:
> http://gouthamanbalaraman.com/blog/bonds-with-spreads-quantlib-python.html,
> everything the same up to the part which sets the bond_engine.
>
> Then instead of using the engine, I used BondFunctions:
> >>> settle_date = fixed_rate_bond.settlementDate(calc_date)
> >>> ql.BondFunctions.cleanPrice(fixed_rate_bond, ts_yield, settle_date)
>
> This returns the clean price of 114.09294985282332, which translates
> to the same NPV =114.18461651948999 on the official site (by adding
> the accrued interest).  So far so good.
>
> Then I ask if the clean price is 101, what's the zspread:
> >>> new_clean_price = 101
> >>> zspread = ql.BondFunctions.zSpread(fixed_rate_bond, new_clean_price, ts_yield, day_count, ql.Compounded, fixed_rate_bond.frequency(), settle_date)
> print(zspread)
>
> This shows the zspread=0.02592546532075354.
>
> Then I add this zspread on top of the original yield curve to obtain a
> new yield curve.  My understanding is that by using this new yield
> curve to price the bond, I should recover the new_clean_price.  But it
> does not:
>
> >>> spread1 = ql.SimpleQuote(zspread)
> >>> spread_handle1 = ql.QuoteHandle(spread1)
> >>> ts_spreaded1 = ql.ZeroSpreadedTermStructure(ts_handle, spread_handle1)
> >>> ql.BondFunctions.cleanPrice(fixed_rate_bond, ts_spreaded1, settle_date)
>
> This resulted clean price is 100.91139815763174, which is about 0.0886
> different from the new_clean_price.  I tried to increase the
> "accuracy" parameter in the ql.BondFunctions.zSpread, but doesn't seem
> to help.
>
> Does anyone know why?  Did I misunderstood ZSpread?  Or did I pass
> wrong parameters in the zSpread function call?  Thanks.
>
> Jian
>
>
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