What is it about?
This paper considers the default probability of American lookback option in a mixed jump-diffusion model, where the underlying asset price has to cross two-sided predetermined strikes to activate the American lookback option. We study a default problem with the bankruptcy time being defined as the first passage time of the underlying asset price. By solving a system of coupled MJD-fBm, we obtain an explicit formula for the Laplace transform of the default time. Some numerical results are given for illustration.
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Why is it important?
Highlights • Default problem with the bankruptcy time. • The first passage time of the underlying asset price. • A system of coupled MJD-fBm. • An explicit formula for the Laplace transform of the default time. • The numerical analysis and the Inverse Laplace transforms.
Perspectives
The pricing formula contains random variables about jump size percent, it is difficult to analytical solutions and hard to implement for path-dependent options.
Zhaoqiang Yang
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This page is a summary of: Default probability of American lookback option in a mixed jump-diffusion model, Physica A Statistical Mechanics and its Applications, February 2020, Elsevier,
DOI: 10.1016/j.physa.2019.123242.
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