Posted by
Luca Berardi on
Mar 01, 2005; 9:27am
URL: http://quantlib.414.s1.nabble.com/Possible-problem-on-bermuda-swaptions-2-tp3621p3627.html
Hi Luigi
I have probably found the source of mispricing in bermuda
swaptions. The problem seems to lie in the new implementation of the
class DiscretizedSwap in QuantLib 0.3.8: in fact the DiscretizedSwap
now updates itself in the following way:
- fixed leg: the fixed coupons are added on the payment dates
- floating leg: the floating coupons are added on the fixing dates.
In QL 0.3.7, instead, the DiscretizedSwap updates both the fixed and
floating leg on the fixing dates.
When pricing a swap with lattices, whether a fixed leg is updated on
payment or fixing dates is just the same, but it does make a
difference when pricing bermuda swaptions. In fact assume to have a
call date at March 1st 2005 and fixing and payment dates (coincident,
for simplicity) of the underlying swap on March 15th.
When rolling back the the swap over the tree we eventually get to
March 1st 2005, and here the swaption apply the exercise condition:
swaption = MAX(discount*previous_swaption_value,value_of_underlying_swap)
But THEN the value of the underlying swap is not correct: indeed the
fixed leg has been updated, since the fixed coupon payment on March
15th has been included, while the floating leg has not been updated
yet, since the floating coupon -to be payed on March 15th 2015- will
be included when the swap is rolled back to March 15th 2014,
i.e. on its corresponding fixing date.
Hence the current implementation of QuantLib bermudan swaptions
overweigths the fixed leg of the underlying swap, clearly bearing a
mispricing.
The problem could be easily fixed by letting the fixed leg of the swap
to be updated on fixing dates, too (which is how things are set in
QuantLib 0.3.7). This also enables to discard the first payment after
the exercise date, which was the issue I raised few messages ago.
Ciao,
Luca
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