  American put options are among the most frequently traded single stock
options, and their calibration is computationally challenging since no
closed-form expression is available. Due to the higher flexibility in
comparison to European options, the mathematical model involves additional
constraints, and a variational inequality is obtained. We use the Heston
stochastic volatility model to describe the price of a single stock option. In
order to speed up the calibration process, we apply two model reduction
strategies. Firstly, a reduced basis method (RBM) is used to define a suitable
low-dimensional basis for the numerical approximation of the
parameter-dependent partial differential equation ($\mu$PDE) model. By doing so
the computational complexity for solving the $\mu$PDE is drastically reduced,
and applications of standard minimization algorithms for the calibration are
significantly faster than working with a high-dimensional finite element basis.
Secondly, so-called de-Americanization strategies are applied. Here, the main
idea is to reformulate the calibration problem for American options as a
problem for European options and to exploit closed-form solutions. Both
reduction techniques are systematically compared and tested for both synthetic
and market data sets.
