This paper studies the critical stock price of American options with continuous dividend yield. We solve the integral equation and derive a new analytical formula in a series form for the critical stock price. American options can be priced and hedged analytically with the help of our critical-stock-price formula. Numerical tests show that our formula gives very accurate prices. With the error well controlled, our formula is now ready for traders to use in pricing and hedging the S&P 100 index options and for the Chicago Board Options Exchange to use in computing the VXO volatility index. © 2010 Wiley Periodicals, Inc.postprin

This paper documents the dynamics of the term structure of the implied volatility (IV) smirk of Chicago Board Options Exchange Volatility Index (VIX) options. Empirical analysis shows that VIX option–IV slope predicts VIX futures returns over the next day to month, outperforms existing investors' perception proxies in the stock and option markets. The empirical finding is rationalized through time‐varying correlation between the VIX and volatility of VIX (VVIX), VIX jumps, and investors' net positions in VIX futures market.