Hallerbach (2004) derives an approximation formula to compute a Black-Scholes implied volatility. This formula is equivalent to equation (7) in Corrado and Miller (1996a), with the substitution of a geometric average of stock and strike prices in place of an arithmetic average. Ceteris paribus...

We examine the forecast quality of Chicago Board Options Exchange (CBOE) implied volatility indexes based on the Standard and Poor's 100 and Nasdaq 100 stock indexes. We find that the forecast quality of CBOE implied volatilities for the Samp;P 100 (VIX) has significantly improved in recent...

The academic literature generally concludes that the Black-Scholes model overstates the value of employee stock options (ESOs). In particular, because ESOs cannot be traded, employee risk aversion often elicits premature exercise. As a result, the ESO is less valuable than a traded option. An...

We test the relation between expected and realized excess returns for the S&P 500 index from January 1994 through December 2003 using the proportional reward-to-risk measure to estimate expected returns. When risk is measured by historical volatility, we find no relation between expected and...