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Questions tagged [sabr]

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

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23 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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35 views

Volatility Smile Extrapolation SABR

I am reading the paper "An Arbitrage-free method for smile extrapolation" by Benaim, Dogson and Kainth from RBS. My question is how to find the free parameters $a, b$ and $c$ in their functional form ...
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0answers
75 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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1answer
52 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
45 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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2answers
96 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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1answer
98 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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0answers
30 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
75 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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1answer
90 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
47 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
185 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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1answer
456 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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0answers
71 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
72 views

SABR - how to calculate theta?

I'm just reading into the SABR model. I've found a few papers on how delta and vega can be calculted (in some different ways), but I have found absolutely nothing on any of the other sensitivities yet....
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1answer
102 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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0answers
250 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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91 views

What's the cutting edge way to model Vol Surfaces?

What class of models do firms on wall street use to estimate the equity index option vol surfaces?
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0answers
111 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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0answers
89 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
247 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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0answers
267 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
450 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
595 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
228 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 ...
3
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1answer
318 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 ...
6
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2answers
246 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 ...
3
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1answer
627 views

SABR in FX market: Advantages / disadvantages

I would like to know if someone could provide a summarized view of the advantages and disadvantages of the SABR model used to price FX options?
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1answer
230 views

SABR model: from calibration to mapping the smile/skew in a graph

Let's say that I have a calibrated SABR model in FX market (eg for Eurodollar options). So I have estimated values of beta, rho, alpha, and vol of vol. How do I map the calibration in a (strike, vol)-...
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1answer
480 views

How does one calibrate a stochastic volatility model?

I will try to use SABR Model to price call options in FX market. What does it mean to calibrate the model? As far as my understanding of the Wikipedia article goes, it means to estimate the parameters....
8
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2answers
490 views

SABR Model Closed Form Solution

I've been researching the SABR model and one of the main benefits it seems is that you can obtain a closed for solution of the implied BS volatility in certain cases. In all the papers I've read, I ...
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2answers
935 views

SABR Implied Volatility and Option Prices

I am trying to understand the SABR model. Specifically, I am having difficulty to understand how to calibrate the model parameters, that is, initial variance, volatility of variance, exponent for ...