Implied Volatility in Black-scholes Model with Garch Volatility

Abstract

The famous Black-Scholes option pricing model is a mathematical description of financial market and derivative investment instruments. In this model volatility is a constant function, where trading option is indeed risky due to random components such as volatility. The notion of non-constant volatility was introduced in GARCH processes. Recently a Black-Scholes model with GARCH volatility has been introduced (Gong et al., 2010).In this article we derive an implied volatility formula for BS-Model with GARCH volatility. In this approach implied volatility patterns are due to market frictions and help us to support the evidence of fat-tailed return distributions against the disputed premise of lognormal returns in Black-Scholes model (Black and Scholes, 1973).