# 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 ...
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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 ...
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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 ...
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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 ...
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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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### 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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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?
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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 ...
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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 ...
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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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