Abstract:We propose a Legendre–Laguerre spectral approximation to price the European and double barrier options in the time-fractional framework. By choosing an appropriate basis function, the spectral discretization is used for the approximation of the spatial derivatives of the time-fractional Black–Scholes equation. For the time discretization, we consider the popular
$L1$
finite difference approximation, which converges with order
$\mathcal {O}((\Delta \tau )^{2-\alpha })$
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