We develop analytic pricing models for options on averages by means of a state-space expansion method. These models augment the class of Asian options to markets where the underlying traded variable follows a mean-reverting process. The approach builds from the digital Asian option on the average and enables pricing of standard Asian calls and puts, caps and floors, as well as other exotica. The models may be used (i) to hedge long period interest rate risk cheaply, (ii) to hedge event risk (regime based risk), (iii) to manage long term foreign exchange risk by hedging through the average interest differential, (iv) managing credit risk exposures, and (v) for pricing specialized options like range-Asians. The techniques in the paper provide several advantages over existing numerical approaches.