Numerical methods for backward Markov chain driven Black-Scholes option pricing

Chi Yan Au, Eric S. Fung, Leevan LING*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The drift, the risk-free interest rate, and the volatility change over time horizon in realistic financial world. These frustrations break the necessary assumptions in the Black-Scholes model (BSM) in which all parameters are assumed to be constant. To better model the real markets, a modified BSM is proposed for numerically evaluating options price-changeable parameters are allowed through the backward Markov regime switching. The method of fundamental solutions (MFS) is applied to solve the modified model and price a given option. A series of numerical simulations are provided to illustrate the effect of the changing market on option pricing.

Original languageEnglish
Pages (from-to)17-33
Number of pages17
JournalFrontiers of Mathematics in China
Volume6
Issue number1
DOIs
Publication statusPublished - Jan 2011

Scopus Subject Areas

  • Mathematics (miscellaneous)

User-Defined Keywords

  • American option
  • backward Markov regime switching
  • European option
  • free boundary problem
  • method of fundamental solutions (MFS)

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