Pathwise moderate deviations for option pricing. (7th November 2019)

• Record Type: Journal Article
• Authors: Jacquier, Antoine; Spiliopoulos, Konstantinos
• Is Part Of: Mathematical finance. Volume 30:Number 2(2020)
• Page Start: 426
• Page End: 463
• Publication Date: 2019-11-07
• Subjects: Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12228
• Languages: English
• ISSNs: 0960-1627

Abstract

Abstract: We provide a unifying treatment of pathwise moderate deviations for models commonly used in financial applications, and for related integrated functionals. Suitable scaling enables us to transfer these results into small‐time, large‐time, and tail asymptotics for diffusions, as well as for option prices and realized variances. In passing, we highlight some intuitive relationships between moderate deviations rate functions and their large deviations counterparts; these turn out to be useful for numerical purposes, as large deviations rate functions are often difficult to compute.