Option valuation and hedging with basis risk (Q2722587)

In his earlier work [Mathematics of derivative securities (M. A. H. Dempster (ed.) and S. R. Pliska (ed.), Cambridge Univer. Press (1997; Zbl 0914.90017)], the author suggested an approach based on utility maximization for pricing options in an incomplete market. Roughly, an option is fairly priced (for a particular investor) if going long or short a small amount of it has a neutral affect on the investor's achievable utility. NEWLINENEWLINENEWLINEIn this paper these ideas are applied to the basis risk problem in a simple setting where there are two assets with correlated \(\log\)-normal price processes. The ``Basis risk'' is the risk that arises when the asset on which an option is written is not available for hedging-usually because there is no liquid market in it and hedging must be done using some ``closely related'' asset. A call option is written on one asset but only the other is used for hedging. In this context, ''hedging'' means solving some utility maximization problem for the mean value of utility function of the portfolio value at a fixed final time.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00036].