Pricing problem and sensitivity analysis of knock-in external barrier options based on uncertain stock model

Yin Gao and Miao Tian

Chaos, Solitons & Fractals, 2024, vol. 187, issue C

Abstract: Knock-in external barrier options as a special kind of barrier options are popular in the option exchange markets, which contain two assets, one decides the payoffs, and the other decides whether the options can be exercised. In this paper, the normal pricing formulas of knock-in external barrier options based on uncertain stock model including down-in call options and up-in put options are derived by means of the fairness principle. To determine how parameters affect the normal price, sensitivity analysis for the normal pricing formulas of down-in call options and up-in put options are presented. Assume that the price of assets are modeled by Liu’s stock model, the explicit pricing formulas for down-in call options and up-in put options are obtained successfully. Meanwhile, the sensitivity analysis for the explicit price of down-in call options and up-in put options are investigated. Moreover, the numerical algorithms and numerical examples for the above explicit pricing formulas of down-in call options and up-in put options are discussed in this paper.

Keywords: Knock-in external barrier option; Uncertain stock model; Liu process; Uncertain theory (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:187:y:2024:i:c:s0960077924009081

DOI: 10.1016/j.chaos.2024.115356

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