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24 votes

What is the importance of alpha, beta, rho in the SABR volatility model?

We created the SABR model because we realized that (a) option values were nonlinear in the volatility, and (b) volatilities are stochastic. This means that if one had an option (or portfolio of ...
Patrick S Hagan's user avatar
17 votes

What is the importance of alpha, beta, rho in the SABR volatility model?

Let's relabel this as What (TF) is SABR? Alpha, Beta and Rho are the point of the model. So explaining them is explaining the model. A model of two processes Unlike earlier models in which the ...
Phil H's user avatar
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9 votes
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SABR Model Pricing Engine in Python QuantLib

Here is a simple example that might be useful. Basically finding parameters for a given section. Some of the parameters might be assumed at start instead of calibrated. ...
David Duarte's user avatar
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8 votes
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What is the market standard for IR option pricing when moving to SOFR

The industry will continue to use SABR and LMM, although in slightly modified versions. You may want to check the following papers to see how the extended model dynamics look like: SABR smiles for RFR ...
Hasek's user avatar
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7 votes
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SABR Calibration: Normal vs Log-Normal Market Data

I think you did something wrong in translating the input to numerics. As pointed out by dm63 normal vols are quoted in basis points. Using equation A.67a) from the Hagan paper you linked we see (...
math's user avatar
  • 1,738
7 votes

SABR beta range

The SABR process is a strict martingale for all values of beta < 1 (in particular, negative betas are fine). If beta = 1, the process is a strict martingale if and only if rho < 0. Under all ...
andrew's user avatar
  • 126
7 votes

What is the importance of alpha, beta, rho in the SABR volatility model?

Unless I am missing the obvious, I do not see the question being answered? In my opinion, trying to understand in simple language what $\alpha, \beta, \rho$ mean requires an explanation what these ...
AKdemy's user avatar
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7 votes

Calibrate a SABR model?

1) The paper Explicit SABR Calibration Through Simple Expansions explains how to calibrate the SABR model in practice. 2) The role of alpha, beta and rho is well explained in the original SABR paper ...
jherek's user avatar
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7 votes
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Introductory material for getting started with local and stochastic volatility modelling

If you are looking for a short introduction into various concepts used in volatility modeling without too much mathematical derivations (although written by a mathematician), I would recommend 'Smile ...
BEQuant's user avatar
  • 428
6 votes

Introductory material for getting started with local and stochastic volatility modelling

You may find A Short Note on Volatility Models an interesting summary providing bird's-eye overview of general ideas in volatility modeling. I would highly recommend SABR and SABR LIBOR Market Models ...
Hasek's user avatar
  • 814
6 votes
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Bartlett's delta gives wrong signs for calls and puts

Bartlett's delta as computed in your code is a simple finite difference (FD), also called bump and reprice, of the Black values. I do not think there is anything wrong here, besides the fact that you ...
AKdemy's user avatar
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5 votes

SABR Normal Volatility when F = K

This is indeed an important issue if you use SABR in production. If I am correct, you'll need this term $$ \chi(\zeta) = \log \left( \frac{\sqrt{1-2\rho\zeta+\zeta^2}-\rho+\zeta}{1-\rho} \right) $$ ...
jChoi's user avatar
  • 1,164
5 votes

SABR Model Closed Form Solution

It comes from Heat Kernel expansion and differential geometry. See Theorem 6 and Section 8 of http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1717676&download=yes
M. Jeunesse's user avatar
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5 votes
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clarification to use collocation methods to get arbitrage free sabr

If I got this right, you get a SABR model from fitting market implied volatilites (from market price via Black) to SABR volatilites (from SABR parameters via formula above). Then you step back and ...
Mats Lind's user avatar
  • 1,412
5 votes

Black Volatility using SABR model

The SABR model represents the stochastic evolution of the price of some kind of assets under the measure for which it is a zero-drift martingale. For Forward contracts it's the so called "Forward ...
LePiddu's user avatar
  • 393
5 votes

SABR model - beta

In my experience, $\beta$ is frequently pre-selected from a priori considerations because there is a large degree of redundancy between $\beta$ and $\rho$ (both affect the vol smile in similar ways). ...
AKdemy's user avatar
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4 votes
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Motivation of the singular perturbation solution formulation for local volatility model

In fact, this is a confusion caused by a sloppy notation. The rigorous version of the setup should be $$A(K)\rightarrow \epsilon A(K).$$ Then we let $x:=\frac{f-K}\epsilon$. The rest is the usual ...
Hans's user avatar
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4 votes
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Understanding the ZABR model (an extension of SABR)

I have found the answer to my own question during the last month where the question have been unanswered The main question: Look at page 9 from "the ODE can be rearranged to $f'(y)=....=F(y,f)$". For ...
Sanjay's user avatar
  • 1,667
4 votes
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Example of complex structured products on FX market?

Here are a few FX structured product examples: All of these can be notes or swaps, notes will pay back the notional at the end and carry no credit risk (and are normally set so that they are worth ...
will's user avatar
  • 2,571
4 votes

Sabr vs Heston for IR swaptions

TL:DR With SABR you can still use your favorite Black-76 / Bachelier formula and improve your hedging strategy pretty much for free. And when trading options there's no good price without a good ...
LePiddu's user avatar
  • 393
4 votes
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Fitting a volatility smile with pySABR -- Python implementation of SABR model

Edit: You need to specify the keyword arguments in your second example The poor calibration of your second example comes from the fact, that you didn't define the keyword arguments in the LNsabr-...
Pleb's user avatar
  • 4,286
4 votes

Sabr Calibration not fitting the market volatility

Well, it looks pretty good to me. The SABR model has only 4 parameters and there is only so much you can do with them. If you have a lot of volatilities, especially if they have a quite irregular ...
Jesper Tidblom's user avatar
3 votes

SABR ATM volatility

In short , this claim does not hold under all circumstances. There are a few ways to break down such approximation. The options under consideration have very long expiry, i.e. $T$ is very large As ...
Xiaotian Deng's user avatar
3 votes

How to show that SABR is log-normal for $\beta=1$ and normal for $\beta=0$?

First and foremost it is important to clarify that the underlying is not necessarily normal/lognormal but for the special cases of $\beta$ the underlying is normal/lognormal Conditioned on a ...
Sanjay's user avatar
  • 1,667
3 votes
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Why do prices/volatilitie differ from those prediced by models, if the models are used for pricing?

The simplest answer is that prices are not derived from the models. Prices are a result of trading in the market and express the sum of the information and opinions of all market participants at the ...
drobertson's user avatar
  • 1,882
3 votes
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Are extended SABR models useful for options with non-negative underlying

You don't want to use the SABR (or an extension) to price equity options or FX options. The lag of mean-reversion in the model's volatility dynamics leads to explosive behavior and to a implied ...
Phun's user avatar
  • 624

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