Re: [Quantlib-users] greeks with swaptionvolcube2

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

I think they use linear interpolation as well. But they have fixed strikes, i.e. imply a sticky strike dynamics, which means the vol does not change when the ATM level changes.

> On 9. Jun 2020, at 13:38, Aleksis Ali Raza <ale...@go...> wrote:
> 
> Thanks Peter - that makes sense: the linear interpolation in strike direction explains it. Btw, this isn’t the case for capfloor vol surfaces so i assume they’re using a different interpolation in strike.
> 
>> On 9 Jun 2020, at 12:01, Peter Caspers <pca...@gm... <mailto:pca...@gm...>> wrote:
>> 
>> Hi Aleksis,  I am just guessing, but from SwaptionVolCube2 you get “sticky moneyness” deltas: If you shift the rates input, the ATM levels in the cube will change. Since the volatilities are set up relative to these ATM levels, the volatility for a given fixed strike (the one from the trade you price) changes under the rate shift as well. Since SwaptionVolCube2 uses a linear interpolation in strike direction, this might cause issues in particular at the points where the vol(strike) - function is non-differentiable.
>> Best Regards, Peter
>> 
>>> On 08 Jun 2020, at 21:22, Aleksis Ali Raza <ale...@go... <mailto:ale...@go...>> wrote:
>>> 
>>> Hi Peter. That’s correct - the delta (and vega,gamma, etc) all smoothen out to normal when I zero out the skew in the volcube.
>>> 
>>> Btw, the jags are still present when using ’Naive’ mode in the GSR calibration.
>>> 
>>> Moreover, what’s more relevant is that they are also present even when just using a simple BachelierSwaptionEngine for the vanilla swaption case so I don’t think it’s model related.
>>> 
>>> FYI, I’m using normal vols throughout (with skew definition essentially a simple +5 normal vols for each 25bp otm - both for payers and recs)
>>> 
>>> In any case, to answer your question reg gsr calibration, I think I'm doing both (a) and (b) - essentially I’ve added a modified NPV attribute to the below-mentioned swaption class. So it’s a simple 'bump up,calc NPV,bump down, calc NPV, take difference’ using this NPV attribute. Maybe i’m missing one of the steps (a) or (b) in this code?
>>> 
>>> def NPV(self):
>>>     engine = ql.Gaussian1dSwaptionEngine(self.model, 64, 7.0, True, False, self.discount_curve)
>>>     basket = self.nsswaption.calibrationBasket(self.swapbase, self.swvolcube, 'MaturityStrikeByDeltaGamma')
>>>     for basket_i in basket:
>>>         ql.as_black_helper(basket_i).setPricingEngine(engine)
>>>     method = ql.LevenbergMarquardt()
>>>     ec = ql.EndCriteria(1000, 10, 1e-8, 1e-8, 1e-8)
>>>     self.model.calibrateVolatilitiesIterative(basket, method, ec)
>>>     npv = self.nsswaption.NPV()*self.position
>>>     return npv
>>> 
>>> 
>>> 
>>>> On Jun 8, 2020, at 7:21 PM, Peter Caspers <pca...@gm... <mailto:pca...@gm...>> wrote:
>>>> 
>>>> Hi Aleksis,
>>>> 
>>>> do you get the jags only when using a smile, i.e. does the delta get smoother when you use an ATM matrix only?
>>>> 
>>>> Another question I have is a) whether you recalibrate the GSR model after each bump and b) whether you recalculate the calibration basket after each bump as well?
>>>> 
>>>> Thanks
>>>> Peter
>>>> 
>>>>> On 08 Jun 2020, at 17:31, Aleksis Ali Raza via QuantLib-users <qua...@li... <mailto:qua...@li...>> wrote:
>>>>> 
>>>>> Sure, essentially it’s run off this class:
>>>>> 
>>>>> class bermudanswaption():
>>>>> 
>>>>>     def __init__(self, calendar,settlement, used_model, swap, ratecurves, index, swvolcube_clean, swapbase,
>>>>>                  mean_reversion,position):
>>>>> 
>>>>>         discount_curve = ratecurves.loc['discountcurve', 'ratecurves']
>>>>>         self.swvolcube = swvolcube_clean
>>>>>         self.swapbase = swapbase
>>>>>         self.used_model = used_model
>>>>>         self.discount_curve = discount_curve
>>>>>         self.position=position
>>>>> 
>>>>>         fixed_schedule=swap.fixedSchedule()
>>>>>         exerciseDates = [calendar.advance(i, -ql.Period('2D')) for i in fixed_schedule][1:-1]
>>>>>         exercise = ql.BermudanExercise(exerciseDates)
>>>>>         stepDates = exerciseDates
>>>>>         self.exerciseDates=exerciseDates
>>>>>         sigmas = [ql.QuoteHandle(ql.SimpleQuote(0.01))]*(1+len(exerciseDates))
>>>>>         self.used_model = used_model
>>>>> 
>>>>>         if settlement == 'physical':
>>>>>             type = 0
>>>>>             method = 1
>>>>>         else:
>>>>>             type = 1
>>>>>             method = 3
>>>>> 
>>>>>         self.nsswaption = ql.NonstandardSwaption(swap, exercise, type, method)
>>>>>         gsr = ql.Gsr(ratecurves.loc[index, 'ratecurves'],
>>>>>                      stepDates, sigmas, [ql.QuoteHandle(ql.SimpleQuote(mean_reversion))])
>>>>>         engine = ql.Gaussian1dNonstandardSwaptionEngine(gsr, 64, 7.0, True, False,
>>>>>                                                         ql.QuoteHandle(ql.SimpleQuote(0)),
>>>>>                                                         discount_curve, 2)
>>>>>         self.engine = ql.Gaussian1dSwaptionEngine(gsr, 64, 7.0, True, False, discount_curve)
>>>>>         self.nsswaption.setPricingEngine(engine)
>>>>>         self.model = gsr
>>>>> 
>>>>> 
>>>>> 
>>>>> 
>>>>>> On 8 Jun 2020, at 15:50, Christofer Bogaso <bog...@gm... <mailto:bog...@gm...>> wrote:
>>>>>> 
>>>>>> Hi, could you please share your python code? Thanks,
>>>>>> 
>>>>>> On Mon, Jun 8, 2020 at 8:00 PM Aleksis Ali Raza via QuantLib-users <qua...@li... <mailto:qua...@li...>> wrote:
>>>>>> Hi. In case anyone has an explanation: I get a jagged behaviour in a my greeks when I define a (what is to my knowledge sensible) swaption smile using swaptionvolcube2.
>>>>>> 
>>>>>> The greeks are being calculated by source bumping (using a 1bp shift for the rate delta, shown below along with the NPV). The behaviour isn’t too sensitive to the bump size.
>>>>>> 
>>>>>> Portfolio 1 consists of a 1y4y otm payer swaption and Portfolio 2 of a same strike 5y otm bermudan swaption with annual calls (both valued using the Hull-White GSR model calibrated to the swaption vol cube with MaturityStrikeByDeltaGamma mode). 
>>>>>> 
>>>>>> The code is in Python.
>>>>>> 
>>>>>> Thanks, Aleksis
>>>>>>  
>>>>>> 
>>>>>> <optionanalysis_rate.png>
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>> 
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