Sensible Sensitivities for the SABR Model

2011 ◽  
Vol 3 (1) ◽  
pp. 25-38
Author(s):  
Messaoud Chibane ◽  
Hong Miao ◽  
Chenghai Xu
Keyword(s):  
Sabr Model

Linking caplets and swaptions prices in the LMM-SABR model

2009 ◽  
Vol 13 (2) ◽  
pp. 19-45 ◽  
Author(s):  
Riccardo Rebonato ◽  
Richard White
Keyword(s):  
Sabr Model

Sensible Sensitivities for the SABR Model

2009 ◽  
Author(s):  
Messaoud Chibane ◽  
Hong Miao ◽  
Chenghai Xu
Keyword(s):  
Sabr Model

scholarly journals Bartlett's Delta in the SABR Model

2017 ◽  
Author(s):  
Patrick Hagan
Keyword(s):  
Sabr Model

Candidate point selection using a self-attention mechanism for generating a smooth volatility surface under the SABR model

2021 ◽  
Vol 173 ◽  
pp. 114640
Author(s):  
Hyeonuk Kim ◽  
Kyunghyun Park ◽  
Junkee Jeon ◽  
Changhoon Song ◽  
Jungwoo Bae ◽  
...  
Keyword(s):  
Attention Mechanism ◽  
Point Selection ◽  
Sabr Model ◽  
Volatility Surface ◽  
Candidate Point

scholarly journals EXACT PRICING AND LARGE-TIME ASYMPTOTICS FOR THE MODIFIED SABR MODEL AND THE BROWNIAN EXPONENTIAL FUNCTIONAL

2011 ◽  
Vol 14 (04) ◽  
pp. 559-578 ◽  
Author(s):  
MARTIN FORDE
Keyword(s):  
Stock Price ◽  
Implied Volatility ◽  
Large Time ◽  
Transition Density ◽  
Closed Form Expression ◽  
Modified Model ◽  
Exponential Functional ◽  
Price Distribution ◽  
Zero Correlation ◽  
Sabr Model

We derive a closed-form expression for the stock price density under the modified SABR model [see section 2.4 in Islah (2009)] with zero correlation, for β = 1 and β < 1, using the known density for the Brownian exponential functional for μ = 0 given in Matsumoto and Yor (2005), and then reversing the order of integration using Fubini's theorem. We then derive a large-time asymptotic expansion for the Brownian exponential functional for μ = 0, and we use this to characterize the large-time behaviour of the stock price distribution for the modified SABR model; the asymptotic stock price "density" is just the transition density p(t, S0, S) for the CEV process, integrated over the large-time asymptotic "density" [Formula: see text] associated with the Brownian exponential functional (re-scaled), as we might expect. We also compute the large-time asymptotic behaviour for the price of a call option, and we show precisely how the implied volatility tends to zero as the maturity tends to infinity, for β = 1 and β < 1. These results are shown to be consistent with the general large-time asymptotic estimate for implied variance given in Tehranchi (2009). The modified SABR model is significantly more tractable than the standard SABR model. Moreover, the integrated variance for the modified model is infinite a.s. as t → ∞, in contrast to the standard SABR model, so in this sense the modified model is also more realistic.

LOCALIZED RADIAL BASIS FUNCTIONS FOR NO-ARBITRAGE PRICING OF OPTIONS UNDER STOCHASTIC ALPHA–BETA–RHO DYNAMICS

2021 ◽  
Vol 63 (2) ◽  
pp. 203-227
Author(s):  
N. THAKOOR
Keyword(s):  
Radial Basis Functions ◽  
Evaluation Method ◽  
Accurate Method ◽  
Basis Functions ◽  
Computational Method ◽  
Absorbing Boundary ◽  
No Arbitrage ◽  
Radial Basis ◽  
Alpha Beta ◽  
Sabr Model

AbstractClosed-form explicit formulas for implied Black–Scholes volatilities provide a rapid evaluation method for European options under the popular stochastic alpha–beta–rho (SABR) model. However, it is well known that computed prices using the implied volatilities are only accurate for short-term maturities, but, for longer maturities, a more accurate method is required. This work addresses this accuracy problem for long-term maturities by numerically solving the no-arbitrage partial differential equation with an absorbing boundary condition at zero. Localized radial basis functions in a finite-difference mode are employed for the development of a computational method for solving the resulting two-dimensional pricing equation. The proposed method can use either multiquadrics or inverse multiquadrics, which are shown to have comparable performances. Numerical results illustrate the accuracy of the proposed method and, more importantly, that the computed risk-neutral probability densities are nonnegative. These two key properties indicate that the method of solution using localized meshless methods is a viable and efficient means for price computations under SABR dynamics.

Gauge Theory of the Sabr Model

2013 ◽  
Author(s):  
David Miles Pfeffer
Keyword(s):  
Gauge Theory ◽  
Sabr Model
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