It is known that actual option prices deviate from the Black-Scholes formula using the same volatility for different strikes. For the S&P 500 index options, we find that these deviations follow a stable pattern and are described by a simple function of at-the-money-forward total volatility. This...

Did the August 2011 European short sale bans on financial stocks accomplish their goals? In order to answer this question, we use stock options' implied volatility skews to proxy for investors' risk aversion. We find that on ban announcement day, risk aversion levels rose for all stocks but more...

† Stock option price approximations are developed for a model which takes both the risk of default and the stochastic volatility into account. The intensity of defaults is assumed to be influenced by the volatility. It is shown that it might be possible to infer the risk neutral default...