Results 11 to 20 of about 1,031 (118)
Asymptotic Implied Volatility at the Second Order with Application to the SABR Model [PDF]
SSRN Electronic Journal, 2009 We provide a general method to compute a Taylor expansion in time of implied volatility for stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is already known, we compute the first order correction exactly at all strikes from the scalar coefficient of the heat kernel expansion.
Louis Paulot
core +8 more sources
A VOLATILITY-OF-VOLATILITY EXPANSION OF THE OPTION PRICES IN THE SABR STOCHASTIC VOLATILITY MODEL [PDF]
International Journal of Theoretical and Applied Finance, 2020 We propose a new type of asymptotic expansion for the transition probability density function (or heat kernel) of certain parabolic partial differential equations (PDEs) that appear in option pricing. As other, related methods developed by Costanzino, Hagan, Gatheral, Lesniewski, Pascucci, and their collaborators, among others, our method is based on ...
Olesya V. Grishchenko +2 more
+9 more sources
ASYMPTOTICS OF THE TIME-DISCRETIZED LOG-NORMAL SABR MODEL: THE IMPLIED VOLATILITY SURFACE [PDF]
Probability in the Engineering and Informational Sciences, 2020 AbstractWe propose a novel time discretization for the log-normal SABR model which is a popular stochastic volatility model that is widely used in financial practice. Our time discretization is a variant of the Euler–Maruyama scheme. We study its asymptotic properties in the limit of a large number of time steps under a certain asymptotic regime which ...
Dan Pirjol, Lingjiong Zhu
+9 more sources
A Note on the Option Price and 'Mass at Zero in the Uncorrelated SABR Model and Implied Volatility Asymptotics' [PDF]
Quantitative Finance, 2020 Gulisashvili et al. [Quant. Finance, 2018, 18(10), 1753-1765] provide a small-time asymptotics for the mass at zero under the uncorrelated stochastic-alpha-beta-rho (SABR) model by approximating the integrated variance with a moment-matched lognormal distribution.
Jaehyuk Choi, Lixin Wu
+10 more sources
Volatility Swap Under the SABR Model [PDF]
, 2013 The SABR model is shortly presented and the volatility swap explained. The fair value for a volatility swap is then computed using the usual theory in financial mathematics. An analytical solution using confluent hypergeometric functions is found. The solution is then verified using Rama Cont's functional calculus.
Simon Bossoney
+6 more sources
Mass at zero in the uncorrelated SABR model and implied volatility asymptotics [PDF]
Quantitative Finance, 2018 15 pages, 2 tables, 8 figures This updated version concentrates on the small- and large-time asymptotic behaviour of the mass at zero in the uncorrelated SABR model. Some geometric considerations regarding the correlated case are provided in a companion paper arXiv:1610 ...
Archil Gulisashvili +2 more
openalex +9 more sources
Static and dynamic SABR stochastic volatility models: Calibration and option pricing using GPUs [PDF]
Mathematics and Computers in Simulation, 2013 For the calibration of the parameters in static and dynamic SABR stochastic volatility models, we propose the application of the GPU technology to the Simulated Annealing global optimization algorithm and to the Monte Carlo simulation. This calibration has been performed for EURO STOXX 50 index and EUR/USD exchange rate with an asymptotic formula for ...
José Luís Fernández +5 more
+8 more sources
Target volatility option pricing in the lognormal fractional SABR model [PDF]
Quantitative Finance, 2019 We examine in this article the pricing of target volatility options in the lognormal fractional SABR model.
Elisa Alòs +3 more
openalex +3 more sources
A LOW-BIAS SIMULATION SCHEME FOR THE SABR STOCHASTIC VOLATILITY MODEL [PDF]
International Journal of Theoretical and Applied Finance, 2012 The Stochastic Alpha Beta Rho Stochastic Volatility (SABR-SV) model is widely used in the financial industry for the pricing of fixed income instruments. In this paper we develop a low-bias simulation scheme for the SABR-SV model, which deals efficiently with (undesired) possible negative values in the asset price process, the martingale property of ...
Bin Chen +2 more
openalex +4 more sources
Target volatility option pricing in lognormal fractional SABR model
, 2018 We examine in this article the pricing of target volatility options in the lognormal fractional SABR model. A decomposition formula by Ito's calculus yields a theoretical replicating strategy for the target volatility option, assuming the accessibilities of all variance swaps and swaptions.
Elisa Alòs +3 more
+6 more sources