Short-time implied volatility of additive normal tempered stable processes

Michele Azzone and Roberto Baviera ()
Additional contact information
Michele Azzone: Politecnico di Milano
Roberto Baviera: Politecnico di Milano

Annals of Operations Research, 2024, vol. 336, issue 1, No 5, 93-126

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 $$\beta $$ β , related to the variance of jumps, and $$\delta $$ δ , related to the smile asymmetry. It has been observed, in option market data, that $$\beta =1$$ β = 1 and $$\delta =-1/2$$ 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 $$\beta =1$$ β = 1 and $$\delta =-1/2$$ δ = - 1 / 2 .

Keywords: Additive process; Volatility surface; Skew; Small-time; Calibration (search for similar items in EconPapers)
JEL-codes: C51 G13 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10479-022-04894-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:336:y:2024:i:1:d:10.1007_s10479-022-04894-y

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-022-04894-y

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().