Simple improvement method for upper bound of American option

Mika Fujii, Koichi Matsumoto, Kengo Tsubota

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper studies the pricing of American options. An upper bound of the price can be made from a martingale and an optimal martingale attains the true price. But it is not easy to find an optimal martingale, and then the improvement of the upper bound is an important problem. In this study, we propose a simple improvement method of the upper bound by stopping times. The stopping times are made from a lower bound process of the continuation value of the American option. We show that a higher lower bound process improves an upper bound more. Finally we show numerically that our method works in the Black-Scholes model.

Original languageEnglish
Pages (from-to)449-466
Number of pages18
JournalStochastics
Volume83
Issue number4-6
DOIs
Publication statusPublished - Aug 1 2011

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American Options
Martingale
Upper bound
Stopping Time
Costs
Lower bound
Black-Scholes Model
Continuation
Pricing

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation

Cite this

Simple improvement method for upper bound of American option. / Fujii, Mika; Matsumoto, Koichi; Tsubota, Kengo.

In: Stochastics, Vol. 83, No. 4-6, 01.08.2011, p. 449-466.

Research output: Contribution to journalArticle

Fujii, Mika ; Matsumoto, Koichi ; Tsubota, Kengo. / Simple improvement method for upper bound of American option. In: Stochastics. 2011 ; Vol. 83, No. 4-6. pp. 449-466.
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