Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/319156 
Year of Publication: 
2022
Citation: 
[Journal:] Annals of Operations Research [ISSN:] 1572-9338 [Volume:] 336 [Issue:] 1 [Publisher:] Springer US [Place:] New York [Year:] 2022 [Pages:] 93-126
Publisher: 
Springer US, New York
Abstract: 
Abstract Empirical studies have emphasized that the equity implied volatility is characterized by a negative skew inversely proportional to the square root of the time-to-maturity. We examine the short-time-to-maturity behavior of the implied volatility smile for pure jump exponential additive processes. An excellent calibration of the equity volatility surfaces has been achieved by a class of these additive processes with power-law scaling. The two power-law scaling parameters are β, related to the variance of jumps, and δ, related to the smile asymmetry. It has been observed, in option market data, that β=1and δ=-1/2. In this paper, we prove that the implied volatility of these additive processes is consistent, in the short-time, with the equity market empirical characteristics if and only if β=1and δ=-1/2.
Subjects: 
Additive process
Volatility surface
Skew
Small-time
Calibration
Persistent Identifier of the first edition: 
Additional Information: 
C51;G13
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version
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