Initial-Boundary Value and LC Problems

You-lan Zhu, Xiaonan Wu, I-Liang Chern and Zhi-zhong Sun
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You-lan Zhu: University of North Carolina
Xiaonan Wu: Hong Kong Baptist University
I-Liang Chern: National Taiwan University
Zhi-zhong Sun: Southeast University

Chapter 8 in Derivative Securities and Difference Methods, 2013, pp 445-534 from Springer

Abstract: Abstract Evaluation of European-style derivatives can be reduced to solving initial value or initial-boundary value problems of parabolic partial differential equations. This chapter discusses numerical methods for such problems. If an American option problem is formulated as a linear complementarity problem, then the only difference between solving a European option and an American option is that if the solution obtained by the partial differential equation does not satisfy the constraint at some point, then the solution of the PDE at the point should be replaced by the value determined from the constraint condition. Such methods are usually referred to as projected methods for American-style derivatives. Therefore, the two methods are very close, and we also study the projected methods in this chapter.

Keywords: Asset Price; Linear Complementarity Problem; Call Option; American Option; European Option (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-1-4614-7306-0_8

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