Pricing of American call options using simulation and numerical analysis / Beh Woan Lin
Consider the American basket call option in the case where there are N underlying assets, the number of possible exercise times prior to maturity is finite, and the vector of asset prices is modeled using a Levy process. A numerical method based on regression and numerical integration is proposed...
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| Summary: | Consider the American basket call option in the case where there are N underlying
assets, the number of possible exercise times prior to maturity is finite, and the vector of
asset prices is modeled using a Levy process. A numerical method based on regression
and numerical integration is proposed to estimate the prices of the American options. In
the proposed method, we make use of the distribution for the vector of asset prices at a
given time t in the future to determine the “important” values of the vector of asset
prices of which the option values should be determined. In determining the option
values at time t, we first perform a numerical integration along the radial direction in the
N-dimensional polar coordinate system. The value thus obtained is expressed via a
regression procedure as a function of the polar angles, and another numerical
integration is performed over the polar angles to obtain the continuation value. The
larger value of the continuation value and the immediate exercise value will then be the
option value. A method is also proposed to estimate the standard error of the computed
American option price. |
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