Re: [Quantlib-users] Pricing a Vanilla EUR swaption to match ICAP premium

[<da...@el...>]

By trial and error:

Passing the shift (0.02) as the final parameter to
ConstantSwaptionVolatility, then using ICAP's shifted black vol (0.272)
gives me a matching premium.

 

From: da...@el... <da...@el...> 
Sent: Monday, 1 November 2021 20:28
To: 'QuantLib users' <qua...@li...>
Subject: [Quantlib-users] Pricing a Vanilla EUR swaption to match ICAP
premium

 

Hi, I am undertaking what on the face of it should be a simple Python task:
replicate the ICAP ATMF cash-settled spot swaption premiums, given their
volatility quotes. I get what seems to be a reasonable number, but that
could just be luck (!).

 

My base swaption is a EUR 1y10y ATMF receiver, as of today, 1st November.

The ATMF is 0.40%, and according to ICAP:
- 'EUR Cash IRR' vol is 187.3

- 'EUR Cash IRR Shifted Black Vol' is 27.2

- 'EUR Shifts' is 2.00

- 'EUR Cash IRR Cal' Normal vol is 65.1

- 'EUR Spot Cash IRR Premium' is 511.0 (for an atmf straddle)

 

If I use this code (I have created curves which generate an atmf agreeing
with 0.40%):

 

    const_vol =
ql.ConstantSwaptionVolatility(2,calendar,ql.ModifiedFollowing,

 
ql.QuoteHandle(ql.SimpleQuote(1.873)), 

 
ql.ActualActual(),ql.ShiftedLognormal)

 

    const_vol_handle = ql.SwaptionVolatilityStructureHandle(const_vol)

 

    blackEngine = ql.BlackSwaptionEngine(discount_curve,const_vol_handle)

 

    swaption = ql.Swaption(parSwap, exercise, ql.Settlement.Cash,
ql.Settlement.ParYieldCurve)

    swaption.setPricingEngine(blackEngine)

 

    print('Swaption px {0:.1f} cents'.format(100*swaption.NPV()))

 

with result:

 

    Swaption px 257.4 cents

 

and price the swaption, I get a premium which is pretty close to ICAP (once
doubled to 514.8), but not quite the same.

 

However, I am not sure how (if?) to incorporate the shift of 2 (% I assume),
which is an optional parameter to ql.ConstantSwaptionVolatility() to handle
negative strikes. If I pass 0.02 as this parameter, then I get a
non-sensical premium: should I be bumping my entire swap curve by 2% before
pricing?

Or perhaps I should just be taking the market premia and backing out the
vol?

Grateful for any guidance on this.

Best wishes,

David Sansom