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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Modelling vol for serial options for SOFR futures
Im trying to model the volatility for serial options on SOFR futures. I'm currently using SABR model to do this.
For a given date, I have both quarterly and serial options. I calculate implied normal ...
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Volatility surface PCA and SABR explanation gap
I am wondering how would the results of PCA on a volatility surface would be used differently than the SABR parameters. Given the first three components of a PCA are related to level, smile and skew, ...
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SABR parameter fitting to ATM normal vol in Quantlib
I’m trying to fit SABR parameters to implied normal vols of options on interest rate futures. I’m attempting this using Quantlib in Python.
This link
https://uk.mathworks.com/help/fininst/calibrating-...
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Using quantlib in python to optimise SABR parameters
I'm trying to use SABR to model volatility smile using QuantLib in python. Can someone provide an easy example of optimising SABR parameters using quantlib and returning a quantlib sabr smile?
I've ...
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Credit Index Options and SABR calibration for smile
I was wondering if it made any theoritical sense to use SABR on credit index options, as we can get implied volatilities from quotes (in Bloomberg or by inversion of Black model). I get that the SABR ...
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Sabr extension with stochastic params
I recall reading an article that discussed an extension of the SABR model, where the model's parameters were suggested to be stochastic, leading to improved volatility surface modeling. Unfortunately, ...
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Selecting volatility for stress scenario
I would like to stress my position in options, changing underlying price $S$ and volatility $\sigma$ at the same time.
Let's assume that after some analysis of the price history I concluded that my ...
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python package for SABR calibration and greeks
pysabr seems to only fit and does not provide greeks.
Curious if anyone used a decent python package that fits SABR model and produces greeks (delta/gamma/vega/theta/volga/vanna). Thanks.
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10D quotes for FX volatility smile calibration
When calibrating fx smile using SABR and Vanna Volga,
Are 10D-RR and 10D-BF used?
Or 25D and ATM quotes are used only?
If 10D is used, which currency pairs use 10D quotes?
If I use 10D quote for ...
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Boundary Conditions of a SABR PDE
I am looking to solve a sabr partial differential equation numerically using finite volume method, but I don't seem to find any information about the boundary condition to apply. Below is the form of ...
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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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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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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, 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 ...
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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}) = \...
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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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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
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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：
...
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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 ...
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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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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 ...
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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 \...
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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 ...
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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/...
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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 ...
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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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