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Questions tagged [sabr]

The Stochastic Alpha Beta Rho (SABR) model is a stochastic volatility model for forward prices, commonly used in the modelling of interest rate derivatives. The alpha, beta and rho in the name are parameters to be calibrated.

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How to solve special ATM case for Hagan approximation?

In Hagan et al's original SABR paper (https://www.next-finance.net/IMG/pdf/pdf_SABR.pdf), how do we reduce (2.17a) to (2.18) for the special ATM case? Could someone help walk me through the algebra? ...
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Calibrating SABR -- Can I calibrate the forward like any other parameter?

Essentially the title to the above. I am using SABR to price caps and floors (as well as options on SOFR futures). I currently have two calibration techniques, the first calibrates based on rho and nu ...
Zac Likes Vol's user avatar
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Monte Carlo simulation with SABR model

I have to price European Options using only the classical Monte Carlo method. The models I have to select are Lévy models and SABR. Consider for instance the simplest Lévy model: a Geometric Brownian ...
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Bumping forward rates in Quantlib for Bartlett SABR greeks

This might be a naive question, but in order to compute the Barlett vega: $$ \frac{d\sigma}{d\alpha} + \frac{d\sigma}{dF}\frac{\rho F^\beta}{\nu}$$ (for forward rate $F$, implied vol $\sigma$, and ...
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Singular Perturbation in Hagan's 2002 SABR paper "Managing Smile Risk"

I'm reading Hagan's 2002 paper Managing Smile Risk originally published on the WILMOTT magazine, and got something confusing. The set up: $P(τ,f,α,K)$ is the solution of the problem as in Equation (A....
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Fitting volatility using SABR

I have been working on generating a volatility surface for options on SOFR futures with the help of the SABR model. I am running into some trouble for low strikes in particular, in that I cannot seem ...
Zac Likes Vol's user avatar
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A question about Hagan's 2002 SABR paper "Managing Smile Risk"

I'm reading Hagan's 2002 paper Managing Smile Risk originally published on the WILMOTT magazine, and got something confusing. The set up: Consider a European call option on an asset $A$ with exercise ...
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Implementations of stochastic collocation for Arbitrage Free SABR

I am currently reading this paper (link) on fitting arbitrage free parameters for SABR using stochastic collocation. Are there any publicly available github repos that implement solutions that are ...
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Change of expansion point for singular perturbation solution in Equivalent Black Volatilities

In the paper Equivalent Black Volatilities, an peturbative solution is derived for the equivalent Black volatility of a vanilla call option under the dynamics $dF_t = a(t) A(F_t) dW_t$ by Taylor ...
Zach Effman's user avatar
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what is the point of SABR model as an interpolation tool if we can already observe the whole vol cube from the market

on BBG and other data providers, it is common that you can find the whole vol surface/cubes. What is the point of the SABR model as an interpolation tool? why cannot people just linear interpolate the ...
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Is SABR model more used as an interpolation method or is used to risk manage option positions in practice?

One can risk manage option positions via sabr model (managing risks w.r.t. the sabr params), or just use sabr as an interpolation method to get black vols and risk manage option positions using black ...
Peaceful's user avatar
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Sabr practical calibration

What practical methods can be employed to address the calibration challenges of the initial SABR model for very far strikes, particularly in the context of pricing CMS, without over-parameterizing the ...
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Volatility Mismatch in SABR Calibration

Problem Statement Hi, I am trying to calibrate SABR on a new asset, which is not 'forward swap rate'. While using the vanillaSABR calibration, I find the parameter 'sigma' (one of model parameters, ...
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Balland - SABR goes normal

To summarise this very long post : please help me understand the undetailed proof of the quoted paper. I am not comfortable using a result I do not fully understand. I am reading Balland & Tran ...
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Volatility Surface Construction: Ask IV, Bid IV and Mid IV

I am presently engaged in a project wherein my objective is to construct a volatility surface utilizing either the SVI parameterization or the SABR model, leveraging real market data. Initially, I ...
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Optimal Fitting Criteria of SABR

I was reading about SABR Model and curious about this. The process of fitting the SABR model involves finding values for the parameters α, β, ρ, ν that minimize the difference between model-implied ...
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How to calculate D(f) in the new lognormal and normal formula in this document : "Explicit SABR Calibration through Simple Expansions"?

I'm currently reading this paper "Explicit SABR Calibration through Simple Expansions" by Fabien Le Floc'h and Gary Kennedy and in the 3rd part when they introduce Andersen & Brotherton-...
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SABR: how to deal with the wings?

I have experimented a bit with the SABR model. In particular I have calibrated it on EURUSD. Obviously, as SABR is a 3 parameter model, it will not fit the 5 market quotes consisting of ATM, 25 delta ...
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SABR, Stochastic collocation and calendar arbitrage

Ok, this is a bit of a long read, so be warned.. I am currently learning about the so called "Stochastic collocation" technique which seem to have been quite popular during recent years for ...
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Hagan's implied vol formula for Normal SABR

I'm sure there's an obvious answer to this question so apologies. But reading through this seminal paper on the SABR model, the author's provide an explicit formula for the (normal) implied vol of a $\...
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Closed form solution to get implied vol from delta with SABR model

Given a set of calibrated SABR parameters, what is the approach to get the implied vol for a given delta ? thanks
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SabrSwaptionVolCube Class in Quantilib Python

Just noticed after upgrading to the most recent version of Quantlib Python that the class ql.SabrSwaptionVolCube is now available. This is a very useful class in that it behaves in very much the same ...
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In-depth derivation of implied volatility in the SABR model

I'm working through the derivation of Hagan's formula (Hagan et al, 2002) for the implied volatility of an option in the SABR model. I'm finding it pretty confusing. Most of my hang-ups are coming ...
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Can you use a forward rate curve to infer the SABR model parameters?

I am currently doing a thesis on a class of SDE parameter inference methods and using the SABR model as an example for inference. I want to extend the application to market data. My question is does ...
FledglingQuant's user avatar
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Bartlett's delta gives wrong signs for calls and puts

There is a paper by Bruce Bartlett introducing a modified delta for SABR model which accounts for the correlation between forward and volatility processes. The main result of the paper is that if $dF$ ...
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SABR model - beta

In the SABR model, the parameter beta largely controls the back-bond behaviour of the model. How do people estimate beta? One approach is to regress atm vol vs forward, i.e. $$\ln(\textrm{atm vol}) = \...
JohnRoper's user avatar
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Sabr Calibration not fitting the market volatility

I am trying to calibrate SABR but I do not fit the given volatility. ...
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2 answers
766 views

Is Local Volatility a function of the Strike or the Underlying price?

Long story cut short: I am asking why the Local Volatility function can be thought of as a function of the underlying, when in fact it appears to be a function of the strike. Additionally, I wonder ...
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From Implied volatility to shifted Black volatility

I don't know who to go from normal to shifted black volatility before calibrating SABR with negative interest rates. I see: "As we know that implied volatilities have a one-to-one relationship ...
Natan Kowalski's user avatar
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What is the market standard for IR option pricing when moving to SOFR

From books it looks like market standards to price IR options, like swaptions, are SABR, LMM or mix of the two (SABR-LMM). But LMM models the forward LIBOR rate. What will happen to it once LIBOR ...
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Why can't the curve find the least squares parameters when I used it in SABR model? (SABR Calibration)

Follow is the SABR function part of my code in python: ...
Hester S's user avatar
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2 answers
689 views

Introductory material for getting started with local and stochastic volatility modelling

Are you able to provide some suggestions for resources to get started with non-flat volatility modelling? The models I am interested in are the likes of CEV, Heston, SABR etc. I have tried looking ...
userPrimeNumber's user avatar
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1 answer
151 views

Pricing & hedging vanilla interest rate options with SABR LMM

Are there any advantages of pricing and hedging plain vanilla interest rate options with more complex SABR LMM instead of simpler SABR model? Should one always go with the SABR LMM as a universal ...
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SABR LMM vs no-arbitrage term structure of SABR parameters

There exists a LIBOR Market Model with stochastic volatility for pricing and hedging exotic (e.g. path-dependent) interest rate options with smile. However let us consider the following approach: ...
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3 answers
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Calibrate the SABR model to the implied volatility surface

I'm currently trying to calibrate the SABR model. The question I have is that when I consider papers and other websites I only come across cases where the SABR parameters are calibrated to the implied ...
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SABR LMM for RFR

Is there a research showing a way to use SABR LMM with new RFRs such as SOFR, i.e. pricing exotic path-dependent RFR derivatives with volatility smile and skew? I'm aware that Looking Forward to ...
Hasek's user avatar
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2 votes
1 answer
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Pricing caps/floors on backward-looking USD SOFR with forward-looking LIBOR model

The payoff of a cap/floor is calculated as a payoff of constitutient caplets/floorlets. The SABR volatility model has the implied volatility approximations of Hagan et al. $$\sigma^f_{IV}\approx \...
Hasek's user avatar
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Relation between SABR parameters and Taylor expansion parameters

Suppose a SABR model framework (with $\beta=1$) $$dF_t=\sigma_t S_t dW^{S}_{t}$$ $$d\sigma_t=\alpha \sigma_t dW^{\sigma}_{t}$$ $$dW^{S}_{t}dW^{\sigma}_{t}=\rho dt$$ I know that the Implied Volatility ...
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Dividend adjustment on SABR formula for interpolating implied volatility

We are using a SABR model to interpolate the implied volatility surface. The model yields a formula for implied volatility that contains the following term: $\ln \left(\frac{K}{F}\right)$ It is ...
Joanna's user avatar
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3 votes
1 answer
291 views

Calibration of a volatility smile model on a partial smile

I'm using a well-known SABR model in order to build an implied volatility surface of caps/floors on a very illiquid market which is entirely missing OTM quotes. What happens to SABR implied smile/...
Hasek's user avatar
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SABR-LMM: best way to perform a MC simulation

I am working on a SABR-LMM model with the following system of SDEs under a numeraire $N$: $$ \begin{align} &\mathrm{d} F_i(t) = \sigma_i (t) (F_i(t) + s)^{\beta} \Big( \mu^f_i (t) \mathrm{d}t ...
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Fitting a volatility smile with pySABR -- Python implementation of SABR model

In order to model some volatility smiles I'm using the python's pySABR package. I ran into a situation when I have two almost identical pieces of code for two different volatility smiles missing the ...
Hasek's user avatar
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Can't fit Bloomberg volatility smile with pysabr. What am I doing wrong?

I want to make sure that I can properly use SABR model on 1-period interest rate options, i.e. caplets, therefore I attempted to get lognormal volatilities for 4%, 6%, ATM, 8%, 10% strikes for 3Mx6M ...
Hasek's user avatar
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Should one calibrate SABR model on caps or caplets?

I want to build a volatility surface for caps on a 3M index implied from SABR model. I have a set of cap normal volatilities for a range of strikes (4%, 6%, 8%, 10% and ATM) and maturities (1, 2, 3, 4 ...
Hasek's user avatar
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How to build a volatility surface for caps from the SABR model?

My end goal is to build a volatility surface for caps. It's well known that SABR model has Hagan approximation formulas for log-normal and normal implied volatilities of options, e.g. caplets, ...
Hasek's user avatar
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How to measure accuracy of SABR volatility surfaces?

I would like to test how accurate are SABR volatility surfaces with respect to historical volatility over a given time period and for a specific equity index. Reading a few papers I realised that one ...
tallsamurai's user avatar
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1 answer
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Sabr vs Heston for IR swaptions

Why is SABR considered the model of choice for swaptions? Is the Heston model not suitable? Does Heston produce unrealistic dynamics with respect to the swaption market?
memegame's user avatar
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Adapt SABR Hagan/Obloj model from swaptions to treasuries options

I am a young intern in a brokerage company and I am currently working on developing a new pricer. I would like to encode a skew-visualisation tool and the best way that appeared to me is the SABR ...
Leos's user avatar
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Cocycle Condition for FX and SABR

I was wondering whether SABR model (or some of its modifications) is actually used by practionarers. Also, if one models the FX forward with SABR, would the cocycle condition be satisfied? That is, if ...
exponantes's user avatar
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Numerical/integration methods within dynamic SABR

I have a question regarding volatility estimates in the dynamic SABR model. It is well known that the original Hagan et al. (2002) approximation formula for the SABR model does not work good for ...
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