
handle: 2381/11790 , 2027.42/92059
In this paper, we apply Carr's randomization approximation and the operator form of the Wiener‐Hopf method to double barrier options in continuous time. Each step in the resulting backward induction algorithm is solved using a simple iterative procedure that reduces the problem of pricing options with two barriers to pricing a sequence of certain perpetual contingent claims with first‐touch single barrier features. This procedure admits a clear financial interpretation that can be formulated in the language of embedded options. Our approach results in a fast and accurate pricing method that can be used in a rather wide class of Lévy‐driven models including Variance Gamma processes, Normal Inverse Gaussian processes, KoBoL processes, CGMY model, and Kuznetsov's β‐class. Our method can be applied to double barrier options with arbitrary bounded terminal payoff functions, which, in particular, allows us to price knock‐out double barrier put/call options as well as double‐no‐touch options.
CGMY Model, Economics, double-no-touch options, Laplace transform, Science, Variance Gamma processes, Normal Inverse Gaussian processes, Processes with independent increments; Lévy processes, KoBoL processes, Wiener‐Hopf Factorization, Double Barrier Options, Derivative securities (option pricing, hedging, etc.), Business, KoBoL Processes, Wiener-Hopf factorization, Double‐No‐Touch Options, Option Pricing, option pricing, Levy processes, CGMY model, Numerical methods (including Monte Carlo methods), double barrier options, Fast Fourier Transform, variance gamma processes, Carr's Randomization, fast Fourier transform, normal inverse Gaussian processes, Carr's randomization, Kuznetsov's β‐Processes, Kuznetsov's ss-processes, Variance Gamma Processes, Lévy processes, Laplace Transform, LéVy Processes, Normal Inverse Gaussian Processes, Mathematics, Finance, Kuznetsov's \(\beta\)-processes
CGMY Model, Economics, double-no-touch options, Laplace transform, Science, Variance Gamma processes, Normal Inverse Gaussian processes, Processes with independent increments; Lévy processes, KoBoL processes, Wiener‐Hopf Factorization, Double Barrier Options, Derivative securities (option pricing, hedging, etc.), Business, KoBoL Processes, Wiener-Hopf factorization, Double‐No‐Touch Options, Option Pricing, option pricing, Levy processes, CGMY model, Numerical methods (including Monte Carlo methods), double barrier options, Fast Fourier Transform, variance gamma processes, Carr's Randomization, fast Fourier transform, normal inverse Gaussian processes, Carr's randomization, Kuznetsov's β‐Processes, Kuznetsov's ss-processes, Variance Gamma Processes, Lévy processes, Laplace Transform, LéVy Processes, Normal Inverse Gaussian Processes, Mathematics, Finance, Kuznetsov's \(\beta\)-processes
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