Questions tagged [sabr]
0
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2answers
74 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 ...
-5
votes
0answers
59 views
Implied Volatility of Heston and SABR Model [closed]
i don`t understand clearly in Heston and SABR Model (which are stochastic models)
I wanna see how to derive implied volatility surface which is
generated by Heston Model.
If I already know heston ...
0
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0answers
36 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-\...
0
votes
0answers
25 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 ...
0
votes
0answers
38 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 ...
3
votes
1answer
82 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 ...
1
vote
0answers
39 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 ...
3
votes
1answer
173 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. ...
0
votes
1answer
274 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 ...
0
votes
0answers
54 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 ...
0
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0answers
58 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....
4
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1answer
96 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.$$
What is the ...
4
votes
0answers
210 views
(C++) Monte Carlo pricer for SABR model to test Hagan / Paulot formulas
I'm trying to test the so-called Hagan formula (p.6 of this paper) and the Paulot formula, order 1 only (eq. (43) p.19 of this paper. For this, i'm trying to use both Euler and Milstein scheme ...
0
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0answers
87 views
What's the cutting edge way to model Vol Surfaces?
What class of models do firms on wall street use to estimate the equity index option vol surfaces?
3
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0answers
102 views
Problem of negative local volatility:
Consider the displaced log-normal process: $$dS(t) = \lambda(t)(a(t)+b(t)S(t))dW(t), S(0) = S_0>0, $$ where $W(t)$ is a one-dimensional Brownian motion.
We suppose that $(\forall t \ge 0) : \...
1
vote
0answers
82 views
Option delta under Black mode vs SABR
Under what scenarios would the Deltas for Options on Bond Futures differ the most between Black vs SABR models ?
3
votes
1answer
231 views
SABR: how often is tuning parameters needed?
This questions is regarding the behaviour of banks and other financial institutions who deal with FX products and use SABR model volatilities to price options.
How often do they change/tune ...
1
vote
0answers
221 views
Relationship between SABR and Heston
What is the relationship between SABR parameters $\sigma, \alpha, \beta, \rho$ and heston parameters $\nu, \kappa, \theta, \xi, \rho$?
How do they influence the smile; skewness, kurtosis, etc? And ...
3
votes
2answers
412 views
SABR beta range
I am thinking of using SABR for non-rate underlyings (eg FX and equity underlyings).
Typically one finds the beta via a regression of historical implied vols vs forwards, since
$$\ln(\textrm{atm ...
1
vote
1answer
579 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 ...
1
vote
2answers
225 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 ...
1
vote
1answer
289 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 ...
3
votes
1answer
199 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
votes
1answer
571 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?
0
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1answer
221 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)-...
0
votes
1answer
450 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....
7
votes
2answers
447 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 ...
2
votes
2answers
864 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 ...
