On short-time behavior of implied volatility in a market model with indexes

2024/02/26 by Huy N. Chau, Duy Nguyen, Chau, Huy N. +3
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Economic theories and models #FOS: Economics and business #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2402.16509

openalex publication_date 2024/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper investigates short-term behaviors of implied volatility of derivatives written on indexes in equity markets when the index processes are constructed by using a ranking procedure. Even in simple market settings where stock prices follow geometric Brownian motion dynamics, the ranking mechanism can produce the observed term structure of at-the-money (ATM) implied volatility skew for equity indexes. Our proposed models showcase the ability to reconcile two seemingly contradictory features found in empirical data from equity markets: the long memory of volatilities and the power law of ATM skews. Furthermore, the models allow for the capture of a new phenomenon termed the quasi-blow-up phenomenon.

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