Questions tagged [sabr]

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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
59 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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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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19 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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28 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/...
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65 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
129 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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82 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
81 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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78 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.
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194 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
328 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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110 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 ...
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1answer
77 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 ...
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2answers
225 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
116 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
210 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 ...
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1answer
199 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 ...
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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 ...
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1answer
321 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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128 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 ...
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1answer
185 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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79 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 ...
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160 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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289 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: $S_t$. ...
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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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61 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 $\mathbb{E}[X(T)^n]$ ...
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149 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 ...
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2answers
354 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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1answer
198 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
332 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 ...
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2answers
558 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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137 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 ...
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1answer
279 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 ...
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2answers
227 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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1answer
165 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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1answer
277 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. ...
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2answers
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 ...
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1answer
364 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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1answer
171 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 ...
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543 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 ...
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173 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) : \...
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156 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 ?
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1answer
400 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 ...
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1answer
664 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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3answers
993 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
976 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 ...
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2answers
265 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 ...
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1answer
475 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 ...
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3answers
434 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 ...