Asymptotic Behavior of Stochastic Volatility Models.
Jorge Zubelli | Souza, Max
stochastic volatility | quantitative finances | mathematical methods in finances
The smile curve and the 'bursty' behavior of volatility is still a challenge and a source of interesting modeling problems in finances. The empirical remark that volatility tends to fluctuate at different levels and seems to mean-revert along a derivative contract life time led many authors to consider stochastic volatility market models. However, such stochastic volatility models introduce difficulties that cannot be analyzed satisfactorily unless one carefully takes into account the different time scales involved. This problem led Fouque et al. to a very effective and practical way of correcting the computed prices in the Black-Scholes model so as to accommodate for the volatility under fast mean reversion. In the present work, we explore a different asymptotic regime of the stochastic volatility model analyzed by Fouque et al, discuss its implications and relevance.