Pricing forward-start style exotic options under uncertain stock models with periodic dividends

Javed Hussain; Saba Shahid; Tareq Saeed; Javed Hussain; Saba Shahid; Tareq Saeed

doi:10.3934/math.20241215

AIMS Mathematics

2024, Volume 9, Issue 9: 24934-24954. doi: 10.3934/math.20241215

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Research article

Pricing forward-start style exotic options under uncertain stock models with periodic dividends

1.
Department of Mathematics, Sukkur-IBA University, Sukkur 65200, Pakistan
2.
Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received: 18 May 2024 Revised: 09 August 2024 Accepted: 19 August 2024 Published: 27 August 2024
MSC : 91G20, 97M30

In this study, we derived pricing formulas for various forward-start style exotic options based on an uncertain stock models with periodic dividends. Specifically, we present valuations for forward-start, Cliquet/Ratchet, and spread options. In addition, we conducted numerical simulations of these formulas and compared them to pricing formulas for the same options based on a dividend-paying stock model driven by standard Brownian motion.
- uncertain calculus,
- canonical process,
- uncertain measure,
- finance,
- uncertain variable,
- option pricing
Citation: Javed Hussain, Saba Shahid, Tareq Saeed. Pricing forward-start style exotic options under uncertain stock models with periodic dividends[J]. AIMS Mathematics, 2024, 9(9): 24934-24954. doi: 10.3934/math.20241215

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Abstract

In this study, we derived pricing formulas for various forward-start style exotic options based on an uncertain stock models with periodic dividends. Specifically, we present valuations for forward-start, Cliquet/Ratchet, and spread options. In addition, we conducted numerical simulations of these formulas and compared them to pricing formulas for the same options based on a dividend-paying stock model driven by standard Brownian motion.

References

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