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arXiv · 2402.16509

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

Huy N. Chau·Duy Nguyen·Thai Nguyen
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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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Huy N. Chau, Duy Nguyen, Thai Nguyen. 2024-02-26. On short-time behavior of implied volatility in a market model with indexes. https://arxiv.org/abs/2402.16509

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