Questions tagged [sabr]

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311 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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1answer
432 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 ...
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1answer
289 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 ...
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1answer
222 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 ...
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0answers
59 views

Does my caplet stripped volatility surface make any sense?

My goal is 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, ...
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0answers
37 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 ...
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1answer
94 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, ...
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0answers
52 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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0answers
63 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 ...
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1answer
128 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?
6
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1answer
353 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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4answers
8k 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 ...
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1answer
80 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 ...
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0answers
61 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 ...
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0answers
55 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....
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0answers
45 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 ...
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0answers
105 views

How to interpolate implied swaption volatilities between maturities for SABR?

I want to interpolate the swaption volatility surface (fixed tenor) in the maturity dimension. I have volatility smiles at times T1 and T2, and would like to get the smile at time T with T1<T<T2 ...
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0answers
151 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 ...
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0answers
142 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 ...
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0answers
96 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 ...
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1answer
150 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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0answers
204 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
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1answer
191 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
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1answer
1k 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
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2answers
406 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 - ...
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1answer
259 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 ...
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0answers
69 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 ...
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0answers
122 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 ...
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1answer
120 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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0answers
72 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 ...
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0answers
32 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 ...
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0answers
119 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 ...
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1answer
205 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, ...
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0answers
156 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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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 ...
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1answer
511 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 ...
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0answers
220 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....
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1answer
1k 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 ...
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2answers
544 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 ...
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3answers
1k 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 ...
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1answer
239 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 ...
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2answers
1k 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-\...
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2answers
314 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 ...
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0answers
95 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.
3
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1answer
298 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 ...
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2answers
408 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
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 ...
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2answers
4k views

SABR Calibration: Normal vs Log-Normal Market Data

This question is about getting some clarification as to how to understand market quotes for normal & log-normal vols together with certain model assumptions. So let us define $C_{BS}(F_0,K,T,\...
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0answers
187 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
108 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 ...