Re: Cash-Settled Swaption Annuity in BlackSwaptionEngine

Posted by Paul Giltinan on
URL: http://quantlib.414.s1.nabble.com/Cash-Settled-Swaption-Annuity-in-BlackSwaptionEngine-tp15810p15812.html

Hi Toby,

Thanks for the link, I must have missed that discussion initially.

I have double-checked the Brigo-Mercurio (2nd edition, section 6.7.2) reference mentioned by Peter Caspers; it seems the formula suggested there is different to the formula in the Mercurio link provided below. According to his website, that paper is from 2009, so maybe the paper is more up-to-date than what appears in the book?

Has anybody else come across this before?

Thanks and regards,
Paul

On 29 August 2014 12:02, Nils Tobias Kramer <[hidden email]> wrote:

Hey Paul,

the pricing is a bit ambiguous as there are many different definitions how to price a cash settled swaption. Here's a link to my (essentially same) question:

http://sourceforge.net/p/quantlib/mailman/message/31940415/

Toby

2014-08-29 12:02 GMT+02:00 Paul Giltinan <[hidden email]>:

Hi,

I have a question about the pricing of cash-settled swaptions using QuantLib::BlackSwaptionEngine.

The BlackSwaptionEngine calculates the annuity term for cash-settled swaptions by constructing a temporary discount curve from the forward swap rate  (see row 118 of blackswaptionengine.cpp). However, this curve is then assigned the same reference date as the regular discount curve, which means that the discounting occurs all the way to the evaluation date.

According to Mercurio (http://www.fabiomercurio.it/cashsettled_note.pdf, equation (3)), this discounting should only be applied as far as the cash settlement date of the swaption. I therefore propose a fix which changes the reference date of the aforementioned swap-implied discount curve and thus implements the pricing formula suggested by Mercurio.

If there are no objections I can provide a patch to fix this (code segment below).

Kind regards,

Paul Giltinan

Current implementation

case Settlement::Cash: {

const Leg& fixedLeg = swap.fixedLeg();

boost::shared_ptr<FixedRateCoupon> firstCoupon =

boost::dynamic_pointer_cast<FixedRateCoupon>(fixedLeg[0]);

DayCounter dayCount = firstCoupon->dayCounter();

Real fixedLegCashBPS =

CashFlows::bps(fixedLeg,

InterestRate(atmForward, dayCount, Compounded, Annual),

false, discountCurve_->referenceDate()) ;

annuity = std::fabs(fixedLegCashBPS/basisPoint);

break;

} Proposed Change case Settlement::Cash: { const Leg& fixedLeg = swap->fixedLeg(); boost::shared_ptr<FixedRateCoupon> firstCoupon = boost::dynamic_pointer_cast<FixedRateCoupon>(fixedLeg[0]); DayCounter dayCount = firstCoupon->dayCounter(); Date swapStartDate = firstCoupon->accrualStartDate(); Real fixedLegCashBPS = CashFlows::bps(fixedLeg, InterestRate(atmForward, dayCount, Compounded, Annual), false, swapStartDate); annuity = discountCurve_->discount(swapStartDate) * std::fabs(fixedLegCashBPS/basisPoint); break; }

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