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VALUATION OF CONTINUOUSLY MONITORED DOUBLE BARRIER OPTIONS AND RELATED SECURITIES
Author(s) -
Boyarchenko Mitya,
Levendorskiĭ Sergei
Publication year - 2012
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2010.00469.x
Subject(s) - exotic option , barrier option , variance gamma distribution , valuation (finance) , valuation of options , inverse gaussian distribution , mathematical economics , binary option , binomial options pricing model , stochastic game , computer science , sequence (biology) , mathematical optimization , mathematics , economics , asian option , econometrics , finance , asymptotic distribution , biology , genetics , mathematical analysis , statistics , distribution (mathematics) , estimator
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.