Questions tagged [sabr]
65
questions
2
votes
0answers
33 views
Explicit expression for option prices in SABR?
I am trying to get a grip of the current state of research regarding option pricing in the SABR model.
Am I correct in that, so far, there is no known general formula for the option price in the SABR ...
1
vote
1answer
82 views
Interpreting SABR calibration model output
Calibrate a SABR model?
Following on from this question, I have used the same market data they attached but am unsure on interpreting the output.
When I plot the SABR probabilities against strike for ...
2
votes
1answer
103 views
Under what measure is the SABR stochastic differential equations
The SABR Model is a CEV (constant elasticity of variance) Cox asset process with correlated lognormal stochastic volatility. A forward rate $F(t,T)$ to time $T$, observed at $t$, and the instantaneous ...
0
votes
0answers
38 views
How to Calibrate SABR parameters by fixing Beta(Quantlib XL/Python)
Unable to find a good example for either Quantlib XL/Python where we can calibrate Alpha, Rho and Nu by fixing Beta. Any help would be appreciated
0
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0answers
34 views
Is there an example on how to build ZABR model in Quantlib Python?
I am relatively new to quantlib. I am trying to build a ZABR model in Quantlib Python and was trying to do it on Excel first. Upon some research, found that it is not available on Excel yet.
However, ...
1
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1answer
110 views
Is there a ZABR model on Quantlib XL
I am relatively new to QuantlibXL and would like to build a ZABR model in excel. But I cant find much help online. Any help would be appreciated
2
votes
1answer
202 views
SABR Model Pricing Engine in Python QuantLib
I am looking for a SABR model pricing engine in Python QuantLib setting. I do know that it exists in C++ version, but not sure if available in Python. Any suggestion/feedback with respect to Python ...
2
votes
2answers
97 views
Black Volatility using SABR model
As per the Wikipedia, the SABR model looks like below -
$dF_t = \sigma_t \left(F_t\right)^{\beta} dW_t$
$d \sigma_t = \alpha \sigma_t d Z_t$
I have 3 questions -
...
1
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0answers
39 views
Intuition behind local volatility curve shapes in interest rate environments
I have some questions regarding the intuition behind shapes for the local volatility (LV) curve as seen in quite popular models. Let's say we have the following generalized stochastic-local volatility ...
0
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0answers
70 views
Bond Options Calibration to market volatility using SABR Model
I'm trying to calibrate bond option implied volatility from SABR model to market volatilities, I tried calibration in python but the smile isn't correctly matching with market volatility?
Any help is ...
1
vote
1answer
70 views
Do all stochastic volatility models capture volatility smile?
I started reading SABR model recently.
In Wiki page, it states that the SABR model can capture volatility smile in derivative market.
However, I do not see how it does so.
1
vote
0answers
51 views
Implied vol expansion for $\lambda$-SABR
Is anyone aware of a good implied volatility expansion formula for $\lambda$-SABR (SABR with mean reversion)?
I am not sure if there is a formula as simple (or just slightly more complex) as the ...
1
vote
0answers
24 views
SABR - several maturities in equities
SABR model is quite popular and given options on a certain forward, you can easily calibrate it. In Fixed Income, the extensions to several tenors typically involve LMM. Is there a popular way to so ...
0
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0answers
29 views
Coherent and convex risk measure for a ZCB portfolio
I have the composition of one ZCB portfolio at the time $\ {t_1,...,t_n}$.
I have to estimate the volatility of the single ZCB following (Bruder et al., p.6, 2011) https://mpra.ub.uni-muenchen.de/...
2
votes
0answers
77 views
Hagan et. al original argument for SABR
In the original SABR paper (Hagan et al 2002 ), the introduction of the famous model is motivated by the observation that local volatility models spot dynamics work the wrong way. As the spot ...
2
votes
1answer
149 views
SABR Calibration
I need to generate the Volatility Surface of call options on S&P500 index, my
dataset contains implied volatilities regarding various expiration dates for various strike prices.
My doubt is, ...
3
votes
0answers
104 views
How are Autocallables modelled?
What models are used to price autocallables ? Should we talk about Heston/SABR models which talking about this topic ? Any reference link is welcome.
1
vote
1answer
110 views
Pnl explain using adjusted SABR delta
When looking at SABR, the starting point for a swaption's delta is the usual:
$\Delta = \partial V/\partial F $
However, since we have expressed our volatility $ \sigma $ as a function of our ...
1
vote
0answers
88 views
How to find the right Shift for the SABR Model
I'm looking for the right approche to find the right Shift for the SABR Model.
4
votes
0answers
201 views
The error term of Hagan's approximation of Black's vol in SABR
Hagans approximation of Black's implied vol in SABR is very! difficult to understand fully. But I want to ask in here if anyone can tell me more about the error term.
Consider the paper:
http://web....
2
votes
1answer
501 views
SABR Implied Vol: Normal Approximation vs Log-Normal Approximation
I am having trouble understanding the difference between the normal and log-normal implied volatilities from Hagans SABR model: http://web.math.ku.dk/~rolf/SABR.pdf.
As far as i understand the main ...
1
vote
0answers
135 views
Black-Scholes vs Blacks model. Which one to use with SABR?
Say I want to compute a call price for a given set of SABR parameters.
I use Hagans approximation and compute $\sigma_B$. The rate is not zero. Should I then compute the option price using
Blacks ...
2
votes
1answer
84 views
$\beta = 1$: Simulation of SABR and whether a solution is *exact*
Quick question regarding the conditional distributions (SABR is just an example here)
Consider
$$dS_t = \sigma_tS_tdW_t$$
$$d\sigma_t = \alpha\sigma_tdV $$
$$dW_tdV_t=\rho dt$$
Hence a SABR process ...
3
votes
2answers
269 views
Does high levels of vol-of-vol parameter in SABR lead to Arbitrage? (Something seems wrong with Hagans formula)
Main question: Do we need to restrict the vol-of-vol parameter in SABR further than $\text{vol-of-vol}>0$ and how do we determine the interval of vol-vol which the model is arbitragefree?
...
2
votes
1answer
142 views
Simulation scheme for SABR beside the standard Euler discretization
QUESTION:
Beside Euler Scheme, is there another more robust (and preferably easy to implement) way to simulate asset path with SABR dynamics?
Simulation that will withstand even for high volatilities....
1
vote
1answer
365 views
Example of complex structured products on FX market?
Lately I have been working a lot with the vol smile and different stochastic volatility models with FX forwards data. Now I want to work with pricing examples through simulations. Can you suggest some ...
0
votes
1answer
234 views
simple SABR model & negative strikes
My goal is to calibrate a simple SABR model.
I do have $tenor$, $expiry$, $forward$ and "market volatilities for strike spread" ranging from -150 to 150 bps.
I think the model can only be ...
4
votes
1answer
2k views
Understanding the ZABR model (an extension of SABR)
http://janroman.dhis.org/finance/SABR/ZABR%20Andreasen.pdf
In this acticle the SABR model is first presented in another form ( see equation 7 in the article ) and then extended to the so called ZABR ...
2
votes
1answer
372 views
zero-shift SABR vega and re-calibration of SABR
I have a zero-shifted SABR model, where I need to confirm if the model is generating the calibration and vega's correctly.
The underlying model is the standard SABR lognormal (there is normal as well)...
1
vote
0answers
141 views
SABR for swaptions
We calibrate SABR on each expiry and tenor combination using market data. (e.g. 1mx10y, 3mx10y etc.) Then how about the non-standard expiry like 2.5mx10y? Do I linear interpolate the alpha, beta, rou ...
3
votes
1answer
220 views
Are extended SABR models useful for options with non-negative underlying
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2731359
http://janroman.dhis.org/finance/SABR/ZABR%20Andreasen.pdf
In the two articles listed above we see several ways to extend the original ...
2
votes
0answers
96 views
The Free Boundary SABR: Natural Extension to Negative Rates
In the paper by Antonov, Konikov and Spector
An alternative approximation for the SABR model is presented.
I'm interested to implement the formula for the ATM swaptions implied volatilities in the ...
6
votes
0answers
164 views
SABR Question: Why does the market take the beta parameter as a constant?
SABR Question
Why does the market take the $\beta$ parameter as a "constant"?
I see most brokers quoting SABR parameters nowadays.
I've seen many banks use $\beta$=0.5 as a rule.
I've seen quants ...
1
vote
0answers
355 views
Is SABR being used in practice for Equity options
Just to be clear: By "in practice" I mean what the banks and other financial companies do.
Do financial companies use SABR for pricing equity options?
Consider a stock with price $t$ being: $S_t$. ...
3
votes
1answer
3k views
Calibrate a SABR model?
How do you calibrate a SABR model using R/Python/Matlab?
Using the data example from: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2725485
1) How does one calibrate the SABR model?
2) How ...
1
vote
0answers
64 views
Analytical formula for the moments of SABR model?
Do analytical formulae exist for the central moments under the SABR model? Assuming dynamics for the forward rate $\{F_t, t \geq 0\}$ under a shifted SABR model. How do we derive $\mathbb{E}[X(T)^n]$ ...
3
votes
0answers
152 views
SABR: implied vol formulas
I noticed that the approximate implied volatilities in Hagan’s 2002 paper (see B69.a and BC9.c, please refer to the paper for the definition of the parameters):
are different from the formulas on ...
1
vote
2answers
404 views
Approximate Hagan formula for SABR model with negative beta
While looking into fixing the $\beta$ parameter (based the following regression: $\text{ln } \sigma^{ATM}_t = \text{ln } \alpha - (1-\beta)\text{ln }F_t$, as explained in West (2004), page 6) before ...
0
votes
1answer
228 views
Calibrate SABR-LMM using only data from Bloomberg?
I'm exploring the SABR-LMM model. In particular, have been trying to study the effect of the parameters and their time evolution.
However, the data seems to be a major issue here. Prices for caps/...
2
votes
3answers
368 views
How to show that SABR is log-normal for $\beta=1$ and normal for $\beta=0$?
For $\beta = 1$ SABR is log-normally distributed and for for $\beta = 0$ SABR is normally distributed. This is a very common property mentioned in almost every paper about SABR. But I can't find the ...
1
vote
2answers
652 views
SABR ATM volatility
The ATM implied volatility is important in SABR when calibrating the model. Let's consider the ATM vol (for a european call option):
$$\sigma =
\frac{\alpha}{f^{1-\beta}} \left[ 1+ \left(\frac{(1-\...
2
votes
0answers
155 views
Checking arbitrage for the SABR model - analytical vs numerical approach
I wish to check if the fitted volatility smile/surface from the SABR model for a fixed time period is arbitrage free. Through my research, I've learnt the following need to be checked:
The RND (risk ...
2
votes
1answer
310 views
SABR Normal Volatility when F = K
Looking at the papers
Arbitrage free SABR (Hagan)
Managing Smile Risk (Hagan)
Explicit SABR Calibration through simple expansions (Floch)
all 3 papers have similar forms for expression for implied ...
4
votes
2answers
252 views
Estimating at-the-money volatility where at-the-money option is absent from the market
I am trying to estimate the intraday ATM volatility in a market where the the strike prices are relatively sparse thus the ATM option may not exist (let's say the closest strike is about 2% away from ...
4
votes
1answer
198 views
Question about derivation of SABR volatility formula in original paper 'Managing Smile Risk' by Hagan et al
I have a question regarding the starting point of the derivation of SABR volatilities formulas in the appendix of the famous paper 'Managing Smile Risk' by Hagan et al.
To derive SABR volatility ...
4
votes
1answer
293 views
Finite Difference method in Matlab for SABR volatility model fails to provide correct option values
Currently, I'm trying to implement a Finite Difference (FD) method in Matlab for my thesis (Quantitative Finance). I implemented the FD method for Black-Scholes already and got correct results. ...
5
votes
2answers
5k views
What is the importance of alpha, beta, rho in the SABR volatility model?
I just read that SABR model is a stochastic volatility model, which attempts to capture the volatility smile in derivatives markets. The name stands for "stochastic alpha, beta, rho", referring to the ...
3
votes
1answer
398 views
Mixing Black Scholes with SABR
I am new to the whole concept of stochastic volatility so I am experimenting with option pricing. I think the concept is really difficult to understand / grasp.
I was wondering if the following ...
5
votes
1answer
183 views
Motivation of the singular perturbation solution formulation for local volatility model
I am puzzled by the motivation of the particular choice of the (singular) perturbation method used in Equivalent Black Volatilities. Equation (A.6a) sets
$$\epsilon:= A(K)\ll 1.$$
What is the ...
6
votes
0answers
578 views
(C++) Monte Carlo pricer for SABR model to test Hagan / Paulot formulas
I'm trying to test the so-called Hagan formula (p.6 of this paper) and the Paulot formula, order 1 only (eq. (43) p.19 of this paper. For this, i'm trying to use both Euler and Milstein scheme ...
