Valuing American Put Options Using Chebyshev Polynomial Approximation
London Metropolitan University Working Paper
23 Pages Posted: 2 Mar 2005
Date Written: February 2005
This paper suggests a simple valuation method based on Chebyshev approximation at Chebyshev nodes to value American put options. It is similar to the approach taken in Sullivan (2000), where the option's continuation region function is estimated by using a Chebyshev polynomial. However, in contrast to Sullivan (2000), the functional is fitted by using Chebyshev nodes. The suggested method is flexible, easy to program and efficient, and can be extended to price other types of derivative instruments. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations. The paper also describes an alternative method based on dynamic programming and backward induction to approximate the option value in each time period.
Keywords: American put options, Bellman equation, Chebyshev polynomial approximation, Chebyshev nodes
JEL Classification: C63, G12
Suggested Citation: Suggested Citation