Finance

We develop a simple closed 0form valuation model for options when the volatility of the underlying asset is stochastic. Out approach differs from previous research in that we model the pricing density directly. We show that implied volatility estimates from the Black-Scholes model can be very misleading, even when at-the-money options are used in the estimation. We also illustrate that the smile effect in index option prices can be explained by allowing changes in volatility to be correlated with index returns.