American type geometric step options

Xiaoyu Xing; Hailiang Yang

doi:10.3934/jimo.2013.9.549

Article Contents

2013, Volume 9, Issue 3: 549-560. Doi: 10.3934/jimo.2013.9.549

This issue Previous Article A conic approximation method for the 0-1 quadratic knapsack problem Next Article A log-exponential regularization method for a mathematical program with general vertical complementarity constraints

American type geometric step options

Xiaoyu Xing^1, and
Hailiang Yang^2,

1.
School of Science, Hebei University of Technology, Tianjin
2.
Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong

Received: September 30, 2011

Revised: August 31, 2012

Published: June 2013

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Abstract

The step option is a special contact whose value decreases gradually in proportional to the spending time outside a barrier of the asset price. European step options were introduced and studied by Linetsky [11] and Davydov et al. [2]. This paper considers American step options, including perpetual case and finite expiration time case. In perpetual case, we find that the optimal exercise time is the first crossing time of the optimal level. The closed price formula for perpetual step option could be derived through Feynman-Kac formula. As for the latter, we present a system of variational inequalities satisfied by the option price. Using the explicit finite difference method we could get the numerical option price.

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Mathematics Subject Classification: Primary: 91B25; Secondary: 60G40.

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References

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