Valuation of Continuously Monitored Double Barrier Options and Related Securities

In this paper, we apply Carr’s randomization approximation and the operator form of theWiener-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.