OPTION PRICING IN ARCH-TYPE MODELS

ARCH models have become popular for modeling financial lime series. Th ey seem, at first, however, to be incompatible with the option pricing approach of Black, Scholes, Merton et al., because they are discrete- time models and possess too much variability. We show that completenes s of the market holds for a broad class of ARCH-type models defined in a suitable continuous-time fashion. As an example we focus on the GAR CH(1,1)-M model and obtain, through our method, the same pricing formu la as Duan, who applied equilibrium-type arguments.