We develop an OLG model aimed at explaining the joint determination of housing prices, rents, and interest rates, in an environment featuring a positive home ownership bias and individual borrowing limits that generate a mismatch between desired and available funds to finance housing purchases. Individual heterogeneity on this mismatch gives rise to three different types of households: renters, landlords ( i.e. buy-to-let investors, who provide the stock of houses for rent) and home buyers who do not participate in the rental market. We investigate the conditions under which two alternative stationary equilibria may coexist: (i) a low valuation equilibrium (LVE) in which landlords do not exhaust their borrowing limits; and (ii) a high valuation one (HVE) where every household is financially constrained at the time of purchasing its housing stock. In a HVE (relative to the LVE) the volume of buy-to-let investment, the price-to-rent ratio and the housing price are higher while the interest rate is lower. Due to binding borrowing constraints, in a HVE further reductions in the interest rate only bear a positive networth effect through a reduction of the cost of repaying outstanding mortgaged debt, which fuels future availability of funds, thus sustaining the higher demand for credit. More generally, coexistence of both types of equilibria provides a rationale for the existence of speculative paths from a LVE to a HVE.