2012/06/13 by Yuri Imamura, Yuta Ishigaki, Imamura, Yuri +5
Economics, Econometrics and Finance · #91G60 #Computational Finance (q-fin.CP) #FOS: Economics and business #Pricing of Securities (q-fin.PR) #msc:91G60 #q-fin.CP #q-fin.PR
paper · pdf · doi:10.48550/arxiv.1206.2934
arxiv created 2012/08/18 · arxiv updated 2012/08/21
In the present paper, we introduce a numerical scheme for the price of a barrier option when the price of the underlying follows a diffusion process. The numerical scheme is based on an extension of a static hedging formula of barrier options. For getting the static hedging formula, the underlying process needs to have a symmetry. We introduce a way to "symmetrize" a given diffusion process. Then the pricing of a barrier option is reduced to that of plain options under the symmetrized process. To show how our symmetrization scheme works, we will present some numerical results applying (path-independent) Euler-Maruyama approximation to our scheme, comparing them with the path-dependent Euler-Maruyama scheme when the model is of the Black-Scholes, CEV, Heston, and (λ) -SABR, respectively. The results show the effectiveness of our scheme.