Currently, there are two types of market models for valuation and risk management of interest rate derivatives, which are the LIBOR and swap market models. In this paper, we introduce generic market models featuring forward rates that span periods other than the classical LIBOR and swap periods. The generic market model generalizes the LIBOR and swap market models. We derive necessary and sufficient conditions for the structure of the forward rates to span an arbitrage-free economy in terms of relative discount bond prices, at all times. We develop generic expressions for the drift terms occurring in the stochastic differential equation (SDE) driving the forward rates under a single pricing measure. Generic market models can be applied to pricing and risk management of constant maturity swaps (CMS) and hybrid coupon swaps, and callable or cancellable versions thereof. A CMS Bermudan swaption allows the holder to enter into a CMS swap. Hybrid coupon swaps feature a payment schedule, where each payment could be a LIBOR rate or a swap rate with arbitrary tenor.