Asymptotic Implied Volatility Smiles in Multiscaling Stochastic Volatility

Summary

The document analyzes implied volatility in a stochastic volatility model designed to capture multiscaling in financial returns. Volatility follows a generalized Ornstein-Uhlenbeck process with super-linear mean reversion. The analysis uses large deviations techniques to derive the asymptotic shape of the implied volatility surface in short-maturity limits and at extreme log-strikes with bounded maturity.

The stated result is that, despite continuous price paths, out-of-the-money implied volatility diverges as maturity becomes small, creating a pronounced smile. This offers a theoretical account of option-smile behavior under the model. The description does not provide parameter estimates, numerical examples, or empirical validation, and it does not specify how well the asymptotic conclusions approximate observed markets at ordinary maturities or strikes.

Key ideas

• The stochastic volatility model incorporates multiscaling behavior in financial series.
• Volatility is modeled with a generalized Ornstein-Uhlenbeck process and super-linear mean reversion.
• Large deviations methods characterize implied volatility for short maturities and extreme strikes.
• The model predicts diverging out-of-the-money implied volatility at short maturities despite continuous price paths.
• The abstract provides theoretical results without reported empirical validation or practical calibration details.

Tags

# The asymptotic smile of a multiscaling stochastic volatility model


# The asymptotic smile of a multiscaling stochastic volatility model









We consider a stochastic volatility model which captures relevant stylized facts of financial series, including the multi-scaling of moments. The volatility evolves according to a generalized Ornstein-Uhlenbeck processes with super-linear mean reversion. Using large deviations techniques, we determine the asymptotic shape of the implied volatility surface in any regime of small maturity $t \to 0$ or extreme log-strike $|κ| \to \infty$ (with bounded maturity). Even if the price has continuous paths, out-of-the-money implied volatility diverges for small maturity, producing a very pronounced smile.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.