Valuation of Continuous-installment Shout Option

DONG Xiaofan; CHEN Yingshan

doi:10.6054/j.jscnun.2023025

Journal of South China Normal University (Natural Science Edition) > 2023 > 55(2): 103-108. > DOI: 10.6054/j.jscnun.2023025

DONG Xiaofan, CHEN Yingshan. Valuation of Continuous-installment Shout Option[J]. Journal of South China Normal University (Natural Science Edition), 2023, 55(2): 103-108. DOI: 10.6054/j.jscnun.2023025

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Valuation of Continuous-installment Shout Option

DONG Xiaofan,
CHEN Yingshan^,

School of Mathematics, South China University of Technology, Guangzhou 510641, China

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Received Date: January 19, 2022
Available Online: June 13, 2023

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Abstract

Abstract

In order to study the pricing problem of continuous-installment options, a parabolic variational inequality that the option price satisfies is derived, and the existence of an explicit expression for its barrier function in a subset of the solution domain is proved. The variational inequality has two free boundaries, one is the optimal shouting boundary, and the other is the optimal stopping boundary. The location and properties of these two free boundaries are discussed through qualitative analysis, and the penalty method is used to solve the variational inequalities so as to give numerical examples with different parameters. The results show that if the risk-free interest rate is greater than the dividend yield, the optimal shouting boundary tends to infinity when the time is far from the maturity date; but as the maturity date approaches, both free boundaries tend to strike prices. In addition, both the shouting right and the installment rate have a significant impact on the free boundaries.
- installment option,
- shout option,
- the parabolic variational inequality,
- the free boundaries

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