Volatility forecasts from current call options

Abstract

We introduce stock options which are now traded actively on many exchanges throughout the world and explain the risk-neutral valuation which is usually assumed when we study the option pricing. This paper shows how to calculate a expectation of a volatility from current call options. We derive a simple condition characterizing the set of all continuous price processes with a given set of option prices. By our method presented in this paper, we show that there is a "smile" in the volatilities of KOSPI200 index options.