FinEquityVolSurface

[mattdoub]

Hi,

Would it be possible to extend the FinEquityVolCurve class into a Surface:
User Inputs (for S&P 500 on 11 Jan 2021)

• value Date (ex: FindDate(2021,1,11) )
• Array of Expires (ex: [FindDate(2021,2,11), FindDate(2021,3,11), FindDate(2021,4,11), FindDate(2021,7,11), FindDate(2021,10,11), FindDate(2022,1,11), FindDate(2023,1,11)])
• Array of Strikes (ex: [3037 3418 3608 3703 3798 3893 3988 4178 4557])
• Array of Vols (ex: [42.94 31.30 25.88 22.94 19.72 16.90 15.31 17.54 25.67,
  37.01 28.25 24.19 21.93 19.57 17.45 15.89 15.34 21.15,
  34.68 27.38 23.82 21.85 19.83 17.98 16.52 15.31 18.94,
  31.41 26.25 23.51 22.05 20.61 19.25 18.03 16.01 15.90,
  29.91 25.58 23.21 22.01 20.83 19.70 18.62 16.63 14.94,
  29.26 25.24 23.03 21.91 20.81 19.73 18.69 16.76 14.63,
  27.59 24.33 22.72 21.93 21.17 20.43 19.71 18.36 16.26] )

This would return a VolSurface object. The volatility method would also be extended to take as input a strike and expiry date.

[domokane]

Sure. Do you have a view on the strike interpolation scheme ? SABR or polynomial or other ?

[mattdoub]

I would use a polynomial interpolation - ideally a SVI implementation

[domokane]

Polynomial in strike or delta ? I have SVI = stoch vol ? I already have SABR. I have started looking at it. I may have something soon. D From: mattdoub<mailto:notifications@github.com> Sent: 11 January 2021 20:42 To: domokane/FinancePy<mailto:FinancePy@noreply.github.com> Cc: Dominic O'Kane<mailto:quant@financepy.com>; Comment<mailto:comment@noreply.github.com> Subject: Re: [domokane/FinancePy] FinEquityVolSurface (#63) I would use a polynomial interpolation - ideally a SVI implementation — You are receiving this because you commented. Reply to this email directly, view it on GitHub<#63 (comment)>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ABJ73PKI5TWXXHKZXM6LVDLSZNIA5ANCNFSM4V5MI4BA>.

[domokane]

OK. I am looking at SVI surfaces.

[mattdoub]

Section 5.1 of the below article describes a fast and robust implementation of the SVI algorithm:
https://zeliade.com/wp-content/uploads/whitepapers/zwp-008-RobustNoArbSSVI.pdf

First the "Slices" are calibrated producing a set of parameters for each expiry/curve provided as input.

Then section 7.2 and 7.3 describes how to interpolate (or extrapolate) for any expiry using the previously calibrated parameters.

This jupyter notebook describes well the parametrisation: (The first section can be dismissed as implied vols are given as input in our case and not derived from option prices).
http://www.cmap.polytechnique.fr/~demarco/files/calibrationParis6/TP_M2_probFin_implied_vol_parametrisation_solutions.ipynb

[domokane]

OK. I will look at this today.

[mattdoub]

SSVI would be polynomial in delta.
SSVI is often used with Listed Option prices as input in the literature which requires a first step to imply the Black-Scholes vols from the prices before then moving to the SSVI polynomial fit.
In this case the vols are given as input so first step is not necessary here.

Further useful resources may be found here:
https://wwwf.imperial.ac.uk/~ajacquie/IC_AMDP/IC_AMDP_Docs/Code/SSVI.pdf

Also happy to take a look at SABR. Is it already available in a VolSurface Class method?

[domokane]

SABR is in the SABR class (shifted and basic) under models. I have just used it in FinFXVolSurfacePlus under market->volatility and I am about to use it again for swaptions. On 12/01/2021 08:42, mattdoub wrote: Cool. SSVI would be polynomial in delta. SSVI is often used with Listed Option prices as input in the literature which requires a first step to imply the Black-Scholes vols from the prices before then moving to the SSVI polynomial fit. In this case the vols are given as input so first step is not necessary here. Further useful resources may be found here: https://wwwf.imperial.ac.uk/~ajacquie/IC_AMDP/IC_AMDP_Docs/Code/SSVI.pdf Also happy to take a look at SABR. Is it already available in a VolSurface Class method? — You are receiving this because you commented. Reply to this email directly, view it on GitHub<#63 (comment)>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ABJ73PK5JXOZZMUNTJEMVWTSZP4PJANCNFSM4V5MI4BA>.

[mattdoub]

SABR is in the SABR class (shifted and basic) under models. I have just used it in FinFXVolSurfacePlus under market->volatility and I am about to use it again for swaptions. On 12/01/2021 08:42, mattdoub wrote: Cool. SSVI would be polynomial in delta. SSVI is often used with Listed Option prices as input in the literature which requires a first step to imply the Black-Scholes vols from the prices before then moving to the SSVI polynomial fit. In this case the vols are given as input so first step is not necessary here. Further useful resources may be found here: https://wwwf.imperial.ac.uk/~ajacquie/IC_AMDP/IC_AMDP_Docs/Code/SSVI.pdf Also happy to take a look at SABR. Is it already available in a VolSurface Class method? — You are receiving this because you commented. Reply to this email directly, view it on GitHub<#63 (comment)>, or unsubscribehttps://github.com/notifications/unsubscribe-auth/ABJ73PK5JXOZZMUNTJEMVWTSZP4PJANCNFSM4V5MI4BA.

Apols meant SSVI polynomia in strike not delta...

[domokane]

Just checked in FinEquityVolatilitySurface. It uses Gatheral's SVI to fit the data you provided. See the test case TestFinEquityVolatilitySurface. I will look at SSVI over the next few days. It's already coded up but not yet wired in.

[domokane]

I am closing this for the moment.

[domokane]

I have added an access function to get the vol called

volatilityFromStrikeDate(K, expiryDate):

[mattdoub]

Looks v good indeed, and it fits well! ;)

Just noticed a tiny bug:
once the curve is calibrated, if you want to see the object in the console it returns an error:
'FinEquityVolSurface' object has no attribute '_atmMethod'

[domokane]

Fixed.

BTW I don't know if I got lucky with the fit as it is unconstrained. I need to build in constraints and no-arb checks. I seeded the longer expiry date fits with the SVI parameters from the previous expiry date which helps.