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, 1 November 2011, Pages
High-order accurate implicit methods for barrier option pricing, , , , a School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africab Kenya Methodist University, P.O Box 1, Nairobi, KenyaThis paper deals with a high-order accurate implicit finite-difference approach to the pricing of barrier options. In this way various types of barrier options are priced, including barrier options paying rebates, and options on dividend-paying-stocks. Moreover, the barriers may be monitored either continuously or discretely. In addition to the high-order accuracy of the scheme, and the stretching effect of the coordinate transformation, the main feature of this approach lies on a probability-based optimal determination of boundary conditions. This leads to much faster and accurate results when compared with similar pricing approaches. The strength of the present scheme is particularly demonstrated in the valuation of discretely monitored barrier options where it yields values closest to those obtained from the only semi-analytical valuation methods available. The scheme is also applied to the analysis of Greeks data such as Delta and Gamma.KeywordsHigh-order accurate scheme; Probability-based optimal boundary; Barrier monitoring; Discretely monitored barriers; Greeks analysis
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An Accurate FFT-Based Algorithm for Bermudan Barrier Option Pricing
DOI: , PP. 89-93
Keywords: ,,
An efficient and accurate numerical method, which is called the CONV method, was proposed by Lord et al in [1] to price Bermudan options. In this paper, this method is applied to price Bermudan barrier options in which the monitored dates may be many times more than the exercise dates. The corresponding algorithm is presented to practical option pricing. Numerical experiments show that this algorithm works very well for different exponential Lévy asset models.
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