Questions tagged [sabr]

The tag has no usage guidance, but it has a tag wiki.

Filter by
Sorted by
Tagged with
1 vote
1 answer
78 views

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 ...
user avatar
  • 13
3 votes
0 answers
50 views

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 ...
user avatar
  • 301
1 vote
1 answer
101 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 \...
user avatar
  • 301
2 votes
0 answers
44 views

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 ...
user avatar
  • 785
1 vote
0 answers
35 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 ...
user avatar
  • 785
3 votes
1 answer
152 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/...
user avatar
  • 301
0 votes
0 answers
25 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 ...
user avatar
  • 301
5 votes
0 answers
131 views

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 ...
user avatar
  • 51
1 vote
1 answer
626 views

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 ...
user avatar
  • 301
0 votes
1 answer
291 views

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 ...
user avatar
  • 301
0 votes
1 answer
100 views

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 ...
user avatar
  • 301
1 vote
1 answer
177 views

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, ...
user avatar
  • 301
1 vote
0 answers
58 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 ...
user avatar
0 votes
0 answers
77 views

Calculation of SABR delta

I have a relatively simple question on the calculation of the SABR delta. I consider the Bartlett's delta (although my question remains the same for the unadjusted SABR delta from Hagan (2002) ). The ...
user avatar
  • 21
0 votes
1 answer
246 views

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?
user avatar
1 vote
0 answers
67 views

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 ...
user avatar
  • 11
1 vote
1 answer
84 views

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 ...
user avatar
1 vote
0 answers
60 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....
user avatar
1 vote
0 answers
56 views

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 ...
user avatar
  • 21
4 votes
0 answers
176 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 ...
user avatar
1 vote
0 answers
193 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 ...
user avatar
  • 127
3 votes
0 answers
106 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 ...
user avatar
1 vote
1 answer
609 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 ...
user avatar
1 vote
1 answer
175 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 ...
user avatar
  • 13
0 votes
0 answers
288 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
user avatar
  • 55
1 vote
1 answer
208 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
user avatar
  • 55
3 votes
1 answer
2k 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 ...
user avatar
2 votes
2 answers
498 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 - ...
user avatar
  • 347
1 vote
0 answers
95 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 ...
user avatar
0 votes
0 answers
136 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 ...
user avatar
1 vote
1 answer
131 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.
user avatar
  • 830
1 vote
0 answers
77 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 ...
user avatar
1 vote
0 answers
38 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 ...
user avatar
1 vote
0 answers
134 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 ...
user avatar
  • 21
2 votes
1 answer
224 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, ...
user avatar
3 votes
0 answers
171 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.
user avatar
  • 31
2 votes
1 answer
294 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 ...
user avatar
1 vote
0 answers
97 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.
user avatar
  • 406
4 votes
0 answers
236 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....
user avatar
  • 1,585
2 votes
1 answer
1k 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 ...
user avatar
  • 23
1 vote
0 answers
196 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 ...
user avatar
2 votes
1 answer
125 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 ...
user avatar
  • 1,585
3 votes
2 answers
443 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? ...
user avatar
  • 1,585
3 votes
1 answer
353 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....
user avatar
  • 1,585
1 vote
1 answer
1k 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 ...
user avatar
  • 1,585
0 votes
1 answer
411 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 ...
user avatar
4 votes
1 answer
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 ...
user avatar
  • 1,585
2 votes
1 answer
522 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)...
user avatar
  • 607
2 votes
0 answers
192 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 ...
user avatar
  • 301
4 votes
1 answer
320 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 ...
user avatar
  • 1,585