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early exercise premium method for pricing American options under the J-model

Financial Innovation 2016年第1期2卷 266-291页

作者： Yacin Jerbi Department of Computer Sciences and Applied Mathematics Ecole Nationale des Ingénieurs de SfaxBPW 3038 SfaxTunisia

Background:This study develops a new model called J-am for pricing American options and for determining the related early exercise boundary(EEB).This model is based on a closed-form solution J-formula for pricing European options,defined in the study by Jerbi(Quantitative Finance,15:2041-2052,2015).The J-am pricing formula is a solution of the Black&Scholes(BS)PDE with an additional function called f as a second member and with limit conditions adapted to the American option *** aforesaid function f represents the cash flows resulting from an early exercise of the ***:This study develops the theoretical formulas of the early exercise premium value related to three American option pricing models called J-am,BS-am,and Heston-am *** three models are based on the J-formula by Jerbi(Quantitative Finance,15:2041-2052,2015),BS model,and Heston(Rev Financ Stud,6:327-343,1993)model,*** study performs a general algorithm leading to the EEB and to the American option price for the three ***:After implementing the algorithms,we compare the three aforesaid models in terms of pricing and the EEB *** particular,we examine the equivalence between J-am and Heston-am as an extension of the equivalence studied by Jerbi(Quantitative Finance,15:2041-2052,2015).This equivalence is interesting since it can reduce a bi-dimensional model to an equivalent uni-dimensional ***:We deduce that our model J-am exactly fits the Heston-am one for certain parameters values to be optimized and that all the theoretical results conform with the empirical *** required CPU time to compute the solution is significantly less in the case of the J-am model compared with to the Heston-am model.

关键词： American option pricing Stochastic volatility model early exercise boundary early exercise premium J-law J-process J-formula Heston model

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