Hi there!I have more an intuitive question. In their 2003 RFS paper, Bakshi, Kapadia, and Madan write "What causes the slope of the individual smiles to reverse its sign?". It appears that for individual stocks, the slope of the implied volatility across different moneyness can be upward sloping (whereas for index options it is always downwards sloping). Has anybody got any intuition why for example an out-of-the-money call could be more expensive than an out-of-the-money put? I am looking for an economic rationale!Any help is appreciated!Thanks in advance!

One example: it's an effect often seen in commodity options. For example, higher oil prices are often associatedwith higher volatility environments. So, energy-related and natural resource related stocksmight sometimes behave the same.regards,

QuoteHas anybody got any intuition why for example an out-of-the-money call could be more expensive than an out-of-the-money put? I am looking for an economic rationale!How about supply and demand. If option market makers as a group short the upper strikes and long the lower strikes, then the usually negative skew could be reversed into a positive skew.

Alan, dopeman, thank you for your kind reply.I know that in natural related stocks there might be this pattern, also in currencies, but I am more interested in single-stocks. I somehow like the demand and supply explanation. But why should I be long the lower strikes as a market-maker? Insurance purposes for the non-market maker? What options would I chose as the market-maker?Any ideas?Thanks a lot!Best.

Investors in index options may have different motivations than investors in single-stock options. While the purchase of an index put option may primarily serve as a portfolio insurance, the purchase of a single stock option may be primarily due to a speculative motivation. This would be the supply/demand explanation. Market makers would price according to their hedging costs, rather than their own demand for options (See Bollen and Whaley, 2004, I believe).Secondly, historic return skews of both indexes and (average) single stocks are positive. The RN return distributions become more negatively skewed as they are transformed by the pricing kernel (as B/K/M point out, excess kurtosis and positive risk aversion suffice as an explanation). As only the systematic component of returns is transformed by the pricing kernel, RN index returns end up with a far lower skew than the RN returns of individual stocks. In fact, as is pointed out in a paper by Mayhew and Stivers (2005, I believe -- sorry, I don't have it in front of me), RN stock returns are the less negatively skewed the greater the idiosyncratic component of their returns is.

I think it's simply an expression of an upwards jump being much more likely on a single stock than on an market index.

It could be because of all the reasons below. supply-demand is related to a change in the markets expectation of the stock's long term "mean". during the dot-com bubble most tech stocks had an inverted skew. common people were levered up by selling puts and buying calls!