Some observations on implied volatility

The observed departures of real world markets from the Black-Scholes model have generated much research activity in academic circles and many practical attempts at handling the problem in industry. With some exceptions, the two groups chose very different approaches to the problem. While academics have been building more complex models based on more general processes for underlying assets,  practitioners have focused on building ad-hoc corrections to the Black-Scholes models.  Both have been adding parameters to the basic model, the academics preferring internal model consistency over the ease of parameter estimation, while finance professionals making the exact opposite tradeoffs. In this talk I will present some theoretical arguments justifying the industry practice of using implied volatilities as a basis for pricing and hedging options.