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

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  • Huy N. Chau
  • Duy Nguyen
  • Thai Nguyen

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 novel phenomenon termed the quasi-blow-up phenomenon.

Suggested Citation

  • Huy N. Chau & Duy Nguyen & Thai Nguyen, 2024. "On short-time behavior of implied volatility in a market model with indexes," Papers 2402.16509, arXiv.org, revised Apr 2024.
    • Handle: RePEc:arx:papers:2402.16509
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    References listed on IDEAS

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