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Counting jumps: does the counting process count?

Ballotta, L. ORCID: 0000-0002-2059-6281, Fusai, G. ORCID: 0000-0001-9215-2586 & Marazzina, D. (2024). Counting jumps: does the counting process count?. Quantitative Finance, pp. 1-20. doi: 10.1080/14697688.2024.2357731


In this paper, we develop a ‘jump diffusion type’ financial model based on renewal processes for the discontinuous part of the risk driver, and study its ability to price options and accurately reproduce the corresponding implied volatility surfaces. In this model, the log-returns process displays finite mean and variance, and non-vanishing skewness and excess kurtosis over the
long period. The proposed construction is parsimonious, and it allows for a simple and intuitive pricing formula for European vanilla options; furthermore, it offers an efficient Monte Carlo sample path generator for the pricing of exotic options. We illustrate the performance of the proposed framework using observed market data, and we study the features of the best fitting
model specifications.

Publication Type: Article
Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in Quantitative Finance, available at:
Publisher Keywords: Option pricing, Jumps, Counting process, Renewal process, Market calibra- tion
Subjects: H Social Sciences > HF Commerce
H Social Sciences > HG Finance
Departments: Bayes Business School
Bayes Business School > Finance
SWORD Depositor:
[thumbnail of QF_BFM_Renewals_May24_final.pdf] Text - Accepted Version
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