Results 11 to 20 of about 129,079 (132)
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
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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
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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
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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
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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
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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
Option Pricing Under the Normal SABR Model with Gaussian Quadratures [PDF]
Social Science Research Network, 2023 The stochastic-alpha-beta-rho (SABR) model has been widely adopted in options trading. In particular, the normal ( β = 0) SABR model is a popular model choice for interest rates because it allows negative asset values.
Jaehyuk Choi, Byoung Ki Seo
semanticscholar +1 more source
Probability Density of Lognormal Fractional SABR Model
Risks, 2022 Instantaneous volatility of logarithmic return in the lognormal fractional SABR model is driven by the exponentiation of a correlated fractional Brownian motion.
Jiro Akahori, Xiaoming Song, Tai-Ho Wang
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Heat Kernels, Solvable Lie Groups, and the Mean Reverting SABR Stochastic Volatility Model
, 2016 We use commutator techniques and calculations in solvable Lie groups to investigate certain evolution Partial Differential Equations (PDEs for short) that arise in the study of stochastic volatility models for pricing contingent claims on risky assets.
Siyan Zhang +2 more
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Deep Reinforcement Learning for Dynamic Stock Option Hedging: A Review
Mathematics, 2023 This paper reviews 17 studies addressing dynamic option hedging in frictional markets through Deep Reinforcement Learning (DRL). Specifically, this work analyzes the DRL models, state and action spaces, reward formulations, data generation processes and ...
Reilly Pickard, Yuri Lawryshyn
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