This analysis demonstrates pricing options with a jump-diffusion model, suggesting q-Gaussians effectively model stock returns.
This paper provides evidence that stock returns, after truncation, might be modeled by a special type of continuous mixtures or normals, so-called q-Gaussians. Negative binomial distributions might model the counts for extreme returns. A generalized jump-diffusion model is proposed, and an explicit option pricing formula is obtained.
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Xinxin Jiang (2025) studied this question.
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