[Quantlib-dev] Jamshidian engine with start delay

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

Hello,

in the JamshidianSwaptionEngine the option expiry date and the value 
date of the underlying swap are handled a bit simplified assuming both 
dates equal (see the warning in the code). Though the impact is usually 
not very big we might want to improve this detail in the library ? See 
below for a possible approach. Thank you Sebastian for our discussions 
on the topic.

Aside I would be interested whether the Jamshidian method is still in 
use for model calibration in the world of multi curve enhanced models 
(where by enhanced I mean something simple like a static spread 
correction) because I believe the generalization of the method to this 
setting is not straightforward. Also I feel that numerical integration 
does nearly a just as efficient and accurate job and it directly allows 
for multiple curve computations. Or do you ignore multi curve in the 
calibration phase and only adjust the curves for the actual pricing ?

Back to Jamshidian and the start delay. Some theoretical background and 
numerical examples can be found here

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2246054

A possible implementation goes as follows. First we need to provide an 
extended zerobond option method, which we can add to AffineModel in 
model.hpp

https://github.com/pcaspers/quantlib/commit/e16b4ea5ffbfe33bd6acd0ee6cb3ecd8a43f72a4
<https://github.com/pcaspers/quantlib/commit/b65c50a1147d6ea386b33e4e09b09901200d71ac>
The default implementation uses the same simplification as mentioned 
above ignoring the bond start delay. To improve the pricing in the 
JamshidianEngine we have to overwrite this method in the model 
implementations for which we want it. For the Hull White model I did it here

https://github.com/pcaspers/quantlib/commit/e8b5912cac2e236fe59a885e8cd1e2ed9243cc47

Finally we have to modify the Jamshidian engine a bit

https://github.com/pcaspers/quantlib/commit/019f37a498846d9a6e89a897300f126c01d6ef86

(maybe we should keep some warning in the code because you are not 
forced to support the start delay in your model implementations)

Not suprisingly the test suite breaks when comparing computation results 
to cached values computed with the simplified engine, so the cached 
values should be updated (given that we believe in the new engine)

1>  Testing Hull-White calibration against cached values...
1>  shortratemodels.cpp(126): error in 
"QuantLib::detail::quantlib_test_case(&ShortRateModelTest::testCachedHullWhite)": 
Failed to reproduce cached calibration results:
1>  calculated: a = 0.0464041, sigma = 0.00579912, f(a) = 0.1158,
1>  expected:   a = 0.0488565, sigma = 0.00593662, f(a) = 0.121599,
1>  difference: a = -0.00245242, sigma = -0.000137495, f(a) = -0.00579896,
1>  end criteria = StationaryFunctionValue

regards
   Peter