Questions tagged [sabr]
90
questions
3
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1
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Hagan's explanation of the Local Volatility model
Long story cut short: I am asking why the Local Volatility function can be thought of as a function of the underlying, when in fact it appears to be the function of the strike.
Long story:
The well-...
- 5,396
0
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1
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163
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From Implied volatility to shifted Black volatility
I don't know who to go from normal to shifted black volatility before calibrating SABR with negative interest rates.
I see: "As we know that implied volatilities have a one-to-one relationship
...
9
votes
1
answer
192
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What is the market standard for IR option pricing when moving to SOFR
From books it looks like market standards to price IR options, like swaptions, are SABR, LMM or mix of the two (SABR-LMM).
But LMM models the forward LIBOR rate. What will happen to it once LIBOR ...
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0
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1
answer
93
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Why can't the curve find the least squares parameters when I used it in SABR model? (SABR Calibration)
Follow is the SABR function part of my code in python：
...
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4
votes
2
answers
533
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Introductory material for getting started with local and stochastic volatility modelling
Are you able to provide some suggestions for resources to get started with non-flat volatility modelling? The models I am interested in are the likes of CEV, Heston, SABR etc.
I have tried looking ...
- 152
1
vote
1
answer
80
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Pricing & hedging vanilla interest rate options with SABR LMM
Are there any advantages of pricing and hedging plain vanilla interest rate options with more complex SABR LMM instead of simpler SABR model? Should one always go with the SABR LMM as a universal ...
- 557
1
vote
1
answer
84
views
SABR LMM vs no-arbitrage term structure of SABR parameters
There exists a LIBOR Market Model with stochastic volatility for pricing and hedging exotic (e.g. path-dependent) interest rate options with smile. However let us consider the following approach:
...
- 557
2
votes
3
answers
297
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Calibrate the SABR model to the implied volatility surface
I'm currently trying to calibrate the SABR model. The question I have is that when I consider papers and other websites I only come across cases where the SABR parameters are calibrated to the implied ...
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0
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116
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SABR LMM for RFR
Is there a research showing a way to use SABR LMM with new RFRs such as SOFR, i.e. pricing exotic path-dependent RFR derivatives with volatility smile and skew?
I'm aware that
Looking Forward to ...
- 557
1
vote
1
answer
296
views
Pricing caps/floors on backward-looking USD SOFR with forward-looking LIBOR model
The payoff of a cap/floor is calculated as a payoff of constitutient caplets/floorlets.
The SABR volatility model has the implied volatility approximations of Hagan et al.
$$\sigma^f_{IV}\approx \...
- 557
2
votes
0
answers
67
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Relation between SABR parameters and Taylor expansion parameters
Suppose a SABR model framework (with $\beta=1$)
$$dF_t=\sigma_t S_t dW^{S}_{t}$$
$$d\sigma_t=\alpha \sigma_t dW^{\sigma}_{t}$$
$$dW^{S}_{t}dW^{\sigma}_{t}=\rho dt$$
I know that the Implied Volatility ...
- 805
1
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0
answers
49
views
Dividend adjustment on SABR formula for interpolating implied volatility
We are using a SABR model to interpolate the implied volatility surface.
The model yields a formula for implied volatility that contains the following term:
$\ln \left(\frac{K}{F}\right)$
It is ...
- 805
3
votes
1
answer
189
views
Calibration of a volatility smile model on a partial smile
I'm using a well-known SABR model in order to build an implied volatility surface of caps/floors on a very illiquid market which is entirely missing OTM quotes. What happens to SABR implied smile/...
- 557
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0
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35
views
Implied volatility surface of an average rate Asian caps
Lets say I have a SABR model where implied volatility is given by semi-analytical Hagan et al. formulas and individual caplets are priced with analytical Black formulas. This model allows me to ...
- 557
6
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0
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157
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SABR-LMM: best way to perform a MC simulation
I am working on a SABR-LMM model with the following system of SDEs under a numeraire $N$:
$$
\begin{align}
&\mathrm{d} F_i(t) = \sigma_i (t) (F_i(t) + s)^{\beta} \Big( \mu^f_i (t) \mathrm{d}t ...
- 428
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1
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1k
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Fitting a volatility smile with pySABR -- Python implementation of SABR model
In order to model some volatility smiles I'm using the python's pySABR package.
I ran into a situation when I have two almost identical pieces of code for two different volatility smiles missing the ...
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1
answer
350
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Can't fit Bloomberg volatility smile with pysabr. What am I doing wrong?
I want to make sure that I can properly use SABR model on 1-period interest rate options, i.e. caplets, therefore I attempted to get lognormal volatilities for 4%, 6%, ATM, 8%, 10% strikes for 3Mx6M ...
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1
answer
144
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Should one calibrate SABR model on caps or caplets?
I want to build a volatility surface for caps on a 3M index implied from SABR model. I have a set of cap normal volatilities for a range of strikes (4%, 6%, 8%, 10% and ATM) and maturities (1, 2, 3, 4 ...
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1
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251
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How to build a volatility surface for caps from the SABR model?
My end goal is to build a volatility surface for caps. It's well known that SABR model has Hagan approximation formulas for log-normal and normal implied volatilities of options, e.g. caplets, ...
- 557
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0
answers
65
views
How to measure accuracy of SABR volatility surfaces?
I would like to test how accurate are SABR volatility surfaces with respect to historical volatility over a given time period and for a specific equity index.
Reading a few papers I realised that one ...
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1
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362
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Sabr vs Heston for IR swaptions
Why is SABR considered the model of choice for swaptions? Is the Heston model not suitable? Does Heston produce unrealistic dynamics with respect to the swaption market?
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0
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74
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Adapt SABR Hagan/Obloj model from swaptions to treasuries options
I am a young intern in a brokerage company and I am currently working on developing a new pricer. I would like to encode a skew-visualisation tool and the best way that appeared to me is the SABR ...
- 11
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1
answer
87
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Cocycle Condition for FX and SABR
I was wondering whether SABR model (or some of its modifications) is actually used by practionarers.
Also, if one models the FX forward with SABR, would the cocycle condition be satisfied? That is, if ...
- 11
1
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0
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76
views
Typical SABR parameter values Equity and FX
Would anyone be so kind to post typical SABR values for equity (e.g. S&P500, maturity 6 months and 1 year) and FX (EURUSD, maturity 6mths and 1 yr) for 'normal' markets and for stressed markets (e....
- 5,167
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0
answers
64
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Numerical/integration methods within dynamic SABR
I have a question regarding volatility estimates in the dynamic SABR model. It is well known that the original Hagan et al. (2002) approximation formula for the SABR model does not work good for ...
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0
answers
209
views
SABR vs Dupire: when to use what?
I was wondering for which products one would use the (AF)SABR model and for which ones Dupire's Local Volatility model.
If I understand correctly, Dupire is by construction Arbitrage-Free but produces ...
- 41
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vote
0
answers
238
views
Can you use the SABR implied volatility in the Black Scholes formula?
The SABR implied volatility is often used as an input in Black's model to price swaptions, caps, and
other interest rate derivatives.
I'm wondering whether you can use the SABR closed form solution of ...
- 127
3
votes
0
answers
114
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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 ...
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2
votes
1
answer
741
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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 ...
1
vote
1
answer
192
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 ...
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0
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354
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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
- 55
1
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1
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239
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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
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3
votes
1
answer
2k
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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 ...
- 81
2
votes
2
answers
598
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 -
...
- 347
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0
answers
120
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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 ...
- 143
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0
answers
147
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
1
answer
141
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.
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0
answers
84
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 ...
- 5,167
1
vote
0
answers
40
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 ...
1
vote
0
answers
168
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 ...
- 21
2
votes
1
answer
248
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
0
answers
188
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.
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2
votes
1
answer
352
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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 ...
- 146
1
vote
0
answers
104
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.
- 466
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0
answers
245
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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....
- 1,585
2
votes
1
answer
1k
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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 ...
- 23
1
vote
0
answers
205
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 ...
- 301
3
votes
1
answer
146
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 ...
- 1,585
3
votes
2
answers
496
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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3
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1
answer
380
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....
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