Questions tagged [sabr]
43
questions
1
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1answer
34 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 ...
2
votes
1answer
79 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?
...
1
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1answer
28 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
55 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
68 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
vote
0answers
52 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 ...
1
vote
1answer
162 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
89 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
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0answers
72 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
76 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
42 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
votes
0answers
130 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
110 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
votes
1answer
588 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
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0answers
48 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
votes
0answers
114 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
1answer
204 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
127 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/...
1
vote
3answers
232 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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1answer
260 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-\...
1
vote
0answers
82 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
157 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
1answer
138 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 ...
1
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0answers
81 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
235 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
votes
1answer
2k 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
196 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
127 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.$$
What is the ...
5
votes
0answers
424 views
(C++) Monte Carlo pricer for SABR model to test Hagan / Paulot formulas
I'm trying to test the so-called Hagan formula (p.6 of this paper) and the Paulot formula, order 1 only (eq. (43) p.19 of this paper. For this, i'm trying to use both Euler and Milstein scheme ...
2
votes
0answers
148 views
Problem of negative local volatility:
Consider the displaced log-normal process: $$dS(t) = \lambda(t)(a(t)+b(t)S(t))dW(t), S(0) = S_0>0, $$ where $W(t)$ is a one-dimensional Brownian motion.
We suppose that $(\forall t \ge 0) : \...
2
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0answers
126 views
Option delta under Black mode vs SABR
Under what scenarios would the Deltas for Options on Bond Futures differ the most between Black vs SABR models ?
4
votes
1answer
290 views
SABR: how often is tuning parameters needed?
This questions is regarding the behaviour of banks and other financial institutions who deal with FX products and use SABR model volatilities to price options.
How often do they change/tune ...
3
votes
0answers
417 views
Relationship between SABR and Heston
What is the relationship between SABR parameters $\sigma, \alpha, \beta, \rho$ and heston parameters $\nu, \kappa, \theta, \xi, \rho$?
How do they influence the smile; skewness, kurtosis, etc? And ...
4
votes
2answers
689 views
SABR beta range
I am thinking of using SABR for non-rate underlyings (eg FX and equity underlyings).
Typically one finds the beta via a regression of historical implied vols vs forwards, since
$$\ln(\textrm{atm ...
1
vote
1answer
832 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
vote
2answers
236 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 ...
3
votes
1answer
390 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
363 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
votes
1answer
826 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
votes
1answer
350 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)-...
1
vote
1answer
635 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....
8
votes
2answers
641 views
SABR Model Closed Form Solution
I've been researching the SABR model and one of the main benefits it seems is that you can obtain a closed for solution of the implied BS volatility in certain cases.
In all the papers I've read, I ...
2
votes
2answers
1k views
SABR Implied Volatility and Option Prices
I am trying to understand the SABR model. Specifically, I am having difficulty to understand how to calibrate the model parameters, that is,
initial variance,
volatility of variance,
exponent for ...
