Rents are the largest component of the Consumer Price Index (CPI) in many countries, making accurate and timely measurements of rental price developments essential for inflation monitoring and policy decisions. Market (asking) rent indices are often available in near real-time and with high detail, but differ substantially from the rents paid by the overall tenant population, as typically measured in the CPI. This paper proposes a model to bridge the gap between asking and all-tenant rents. First, using rental-unit listings for Switzerland, we construct timely, granular, and high-frequency indices of asking rents. Second, using a probabilistic model that accounts for the duration of tenants' stays, we estimate all-tenant rents based on historical asking rents. Additionally, we incorporate rent changes during ongoing tenancies. For Switzerland, this corresponds to adjustments permitted under Swiss tenancy law in response to changes in the mortgage reference rate and inflation. This allows us to provide weekly, real-time, and highly disaggregated estimates of all-tenant rents, which are highly correlated with the official quarterly survey-based rental index in the Swiss CPI. Our approach provides a tool for timely rental price monitoring and forecasting that can be adapted for use in other countries.