5 Stochastic volatility
1996; Elsevier BV; Linguagem: Inglês
10.1016/s0169-7161(96)14007-4
ISSN1875-7448
AutoresÉric Ghysels, Andrew Harvey, Éric Renault,
Tópico(s)Complex Systems and Time Series Analysis
ResumoThe class of stochastic volatility (SV) models has its roots in both, mathematical finance and financial econometrics. In fact, several variations of SV models originated from research looking at very different issues. Volatility plays a central role in the pricing of derivative securities. The Black-Scholes model for the pricing of an European option is by far the most widely used formula even when the underlying assumptions are known to be violated. The Black-Scholes model predicts a flat term structure of volatilities. In reality, the term structure of at-the-money implied volatilities is typically upward sloping when short term volatilities are low and the reverse when they are high. The Black-Scholes model is taken as a reference point from which several notions of volatility are presented. Several stylized facts regarding volatility and option prices are also presented. Both sections set the scene for a formal framework defining stochastic volatility. The chapter introduces the statistical models of stochastic volatility.
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