Questions tagged [sabr]
53
questions
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0answers
27 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
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0answers
51 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
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1answer
108 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
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0answers
66 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
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1answer
50 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
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0answers
75 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
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0answers
176 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....
1
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1answer
195 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
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0answers
77 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
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1answer
71 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
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2answers
190 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?
...
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1answer
95 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
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1answer
113 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
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1answer
155 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 ...
1
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0answers
66 views
Why quote call options in terms of implied volatility of the Black-Scholes model?
I came across this seminal paper on SABR model where the value of the call option is computed (eq. A.52).
After the dollar value of the option has been derived, a lot of effort is being put to ...
4
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1answer
1k 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
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1answer
259 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)...
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0answers
115 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
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1answer
158 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
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0answers
70 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 ...
5
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0answers
156 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 ...
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0answers
227 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: $S_t$. ...
2
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1answer
2k 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 ...
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0answers
58 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 $\mathbb{E}[X(T)^n]$ ...
2
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0answers
135 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
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2answers
302 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
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1answer
174 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/...
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3answers
312 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
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2answers
454 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
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0answers
125 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
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1answer
241 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
205 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 ...
2
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1answer
133 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
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1answer
267 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. ...
4
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1answer
4k 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
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1answer
321 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
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1answer
156 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.$$
What is the ...
5
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0answers
513 views
(C++) Monte Carlo pricer for SABR model to test Hagan / Paulot formulas
I'm trying to test the so-called Hagan formula (p.6 of this paper) and the Paulot formula, order 1 only (eq. (43) p.19 of this paper. For this, i'm trying to use both Euler and Milstein scheme ...
2
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0answers
157 views
Problem of negative local volatility:
Consider the displaced log-normal process: $$dS(t) = \lambda(t)(a(t)+b(t)S(t))dW(t), S(0) = S_0>0, $$ where $W(t)$ is a one-dimensional Brownian motion.
We suppose that $(\forall t \ge 0) : \...
2
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0answers
153 views
Option delta under Black mode vs SABR
Under what scenarios would the Deltas for Options on Bond Futures differ the most between Black vs SABR models ?
4
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1answer
377 views
SABR: how often is tuning parameters needed?
This questions is regarding the behaviour of banks and other financial institutions who deal with FX products and use SABR model volatilities to price options.
How often do they change/tune ...
4
votes
1answer
578 views
Relationship between SABR and Heston
What is the relationship between SABR parameters $\sigma, \alpha, \beta, \rho$ and heston parameters $\nu, \kappa, \theta, \xi, \rho$?
How do they influence the smile; skewness, kurtosis, etc? And ...
5
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3answers
902 views
SABR beta range
I am thinking of using SABR for non-rate underlyings (eg FX and equity underlyings).
Typically one finds the beta via a regression of historical implied vols vs forwards, since
$$\ln(\textrm{atm ...
1
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1answer
932 views
SABR calibration in R. How to estimate rho and nu so sum of squared errors is minimized
I start with predefined beta and alpha. Then I want to find rho and nu so the Sum of Squared Errors is minimized. By SSE I mean the difference between my model estimated volatilities and observed ...
1
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2answers
249 views
Why do prices/volatilitie differ from those prediced by models, if the models are used for pricing?
I am wondering how traders come up with prices that are not perfectly explained by the models common for the respective products they are trading. If they use a pricing library, this library should ...
4
votes
1answer
456 views
Shifted SABR for negative strikes
I am trying to apply SABR on EUR inflation caplets, with positive forward and negative strikes. Classical BS pricing is undefined, and so is SABR. I have read about the shifted SABR, which is supposed ...
9
votes
3answers
413 views
clarification to use collocation methods to get arbitrage free sabr
I'm reading the following two papers (first, second) which suggest a so called "stochastic collocation method" to obtain an arbitrage free volatility surface very close to an initial smile stemming ...
3
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1answer
991 views
SABR in FX market: Advantages / disadvantages
I would like to know if someone could provide a summarized view of the advantages and disadvantages of the SABR model used to price FX options?
2
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1answer
422 views
SABR model: from calibration to mapping the smile/skew in a graph
Let's say that I have a calibrated SABR model in FX market (eg for Eurodollar options). So I have estimated values of beta, rho, alpha, and vol of vol. How do I map the calibration in a (strike, vol)-...
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1answer
822 views
How does one calibrate a stochastic volatility model?
I will try to use SABR Model to price call options in FX market. What does it mean to calibrate the model? As far as my understanding of the Wikipedia article goes, it means to estimate the parameters....
