Questions tagged [sabr]

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(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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0answers
152 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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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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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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157 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.
3
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1answer
312 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....
3
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163 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 ...
3
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0answers
189 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
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179 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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116 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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237 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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183 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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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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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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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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46 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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145 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 ...
1
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1answer
436 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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70 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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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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33 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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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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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.
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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 ...
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0answers
494 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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73 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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39 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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63 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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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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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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207 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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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 ...