Chebyshev polynomial approximation to approximate partial differential equations

7. Conclusions

In this study we suggest a simple way to approximate partial differential equations
suggesting a method based on Chebyshev approximation at Chebyshev nodes. We
provide two empirical examples. The first example consisted in pricing an European put
option. The second example consisted in solving an optimal stopping problem. In the last
example the proposed methodology did not use determinist nodes to approximate the
functional but rather stochastic ones. Our method is simple to apply and extend and
provide a reliable framework which can be applied either to price more complex
derivative instruments or used in many interesting cases in economics. We leave this on
the agenda for future research.

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