  A long-standing issue in mathematical finance is the speed-up of pricing
options, especially multi-asset options. A recent study has proposed to use
tensor train learning algorithms to speed up Fourier transform (FT)-based
option pricing, utilizing the ability of tensor networks to compress
high-dimensional tensors. Another usage of the tensor network is to compress
functions, including their parameter dependence. In this study, we propose a
pricing method, where, by a tensor learning algorithm, we build tensor trains
that approximate functions appearing in FT-based option pricing with their
parameter dependence and efficiently calculate the option price for the varying
input parameters. As a benchmark test, we run the proposed method to price a
multi-asset option for the various values of volatilities and present asset
prices. We show that, in the tested cases involving up to 11 assets, the
proposed method is comparable to or outperforms Monte Carlo simulation with
$10^5$ paths in terms of computational complexity, keeping the comparable
accuracy.
