24
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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 ...
- 491
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 ...
- 3,679
9
votes
Accepted
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.
...
- 5,845
8
votes
Accepted
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 ...
- 853
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 ...
- 126
7
votes
Accepted
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 (...
- 1,738
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 ...
- 1,444
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 ...
- 9,419
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 ...
- 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 ...
- 853
6
votes
Accepted
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 ...
- 9,419
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
$$ \chi(\zeta) = \log \left( \frac{\sqrt{1-2\rho\zeta+\zeta^2}-\rho+\zeta}{1-\rho} \right) $$
...
- 1,194
5
votes
Accepted
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 ...
- 1,422
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 ...
- 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).
...
- 9,419
4
votes
Accepted
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 ...
- 2,806
4
votes
Accepted
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 ...
- 1,667
4
votes
Accepted
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 ...
- 2,591
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 ...
- 393
4
votes
Accepted
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-...
- 4,726
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 ...
- 731
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 ...
- 1,667
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 ...
3
votes
Accepted
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 ...
- 1,892
3
votes
Accepted
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 ...
- 624
3
votes
Accepted
Is there a ZABR model on Quantlib XL
ZABR classes are currently only in C++ and Python via SWIG, at least to my knowledge. QuantlibXL is generally not as quick to receive updates to developments in the C++ library because a substantial ...
- 1,456
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