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A NEW STOPPING PROBLEM AND THE CRITICAL EXERCISE PRICE FOR AMERICAN FRACTIONAL LOOKBACK OPTION IN A SPECIAL MIXED JUMP-DIFFUSION MODEL

Published online by Cambridge University Press:  21 September 2018

Zhaoqiang Yang Open the ORCID record for Zhaoqiang Yang [Opens in a new window]
Zhaoqiang Yang*
Affiliation:
Library and School of Statistics, Lanzhou University of Finance and Economics Lanzhou 730101, China E-mail: [email protected] or [email protected]
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Abstract

A new stopping problem and the critical exercise price of American fractional lookback option are developed in the case where the stock price follows a special mixed jump diffusion fractional Brownian motion. By using Itô formula and Wick-Itô-Skorohod integral a new market pricing model is built, and the fundamental solutions of stochastic parabolic partial differential equations are deduced under the condition of Merton assumptions. With an optimal stopping problem and the exercise boundary, the explicit integral representation of early exercise premium and the critical exercise price are also derived. Numerical simulation illustrates the asymptotic behavior of this critical boundary.

Keywords

asymptotic behaviorfundamental solutionsmixed jump-diffusion fractional brownian motionoptimal stopping problemwick-itô-skorohod integral
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Issue 1 , January 2020 , pp. 27 - 52
Copyright
Copyright © Cambridge University Press 2018 

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