Initial-Boundary Value and LC Problems

  • You-lan Zhu
  • Xiaonan Wu
  • I-Liang Chern
Part of the Springer Finance book series (FINANCE)


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.


Option Price Linear Complementarity Problem Call Option American Option European Option 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • You-lan Zhu
    • 1
  • Xiaonan Wu
    • 2
  • I-Liang Chern
    • 3
  1. 1.Department of MathematicsUniversity of North Carolina at CharlotteCharlotteUSA
  2. 2.Department of MathematicsHong Kong Baptist UniversityKowloon Tong, Hong KongChina
  3. 3.Department of MathematicsNational Taiwan UniversityTaipei, TaiwanChina

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