It is well known that the pattern of implied volatilities in foreign currency
options forms a smile shape which is referred to as a volatility smile. On the
other hand, the volatility skew is a general pattern of implied volatilities in
equity options. In this paper, we consider the Carr-Geman-Madan valuation
of options in incomplete markets on which the preference structure of the
market participants are reflected. Through a simple continuous static no
arbitrage extension, we examine how the smiles and skews are related.