Pricing Options With Curved Boundaries

Naoto Kunitomo*, Masayuki Ikeda

*この研究の対応する著者

研究成果査読

155 被引用数 (Scopus)

抄録

This paper provides a general valuation method for the European options whose payoff is restricted by curved boundaries contractually set on the underlying asset price process when it follows the geometric Brownian motion. Our result is based on the generalization of the Levy formula on the Brownian motion by T. W. Anderson in sequential analysis. We give the explicit probability formula that the geometric Brownian motion reaches in an interval at the maturity date without hitting either the lower or the upper curved boundaries. Although the general pricing formulae for options with boundaries are expressed as infinite series in the general case, our numerical study suggests that the convergence of the series is rapid. Our results include the formulae for options with a lower boundary by Merton (1973), for path‐dependent options by Goldman, Sossin, and Gatto (1979), and for some corporate securities as special cases.

本文言語English
ページ(範囲)275-298
ページ数24
ジャーナルMathematical Finance
2
4
DOI
出版ステータスPublished - 1992
外部発表はい

ASJC Scopus subject areas

  • 会計
  • 財務
  • 社会科学(その他)
  • 経済学、計量経済学
  • 応用数学

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