Why do multiple LIBOR curves exist?

A summary of what I found without going too much into the technical details.Photo by Jon Cellier on UnsplashThe London InterBank Offered Rate (LIBOR) is an interest rate at which banks charge each other in the interbank market. It is a primary benchmark for short-term interest rates around the world.The LIBOR was previously known as the British Bankers’ Association (BBA) LIBOR. Now that the responsibility for its administration was transferred to the Intercontinental Exchange (ICE), it is also known as the ICE LIBOR. The LIBOR is published every London business day for 5 currencies (USD, GBP, EUR, CHF and JPY) for 7 different tenors (O/N, 1W, 1M, 2M, 3M, 6M and 12M).I haven’t been too familiar with the intricacies of the LIBOR. What brought my attention to this topic was an interview question asking me to explain this equation:Implied forward rate equationThis is the relationship between the implied forward rate between two points in time (T0 and T1) as of time t, in terms of discount factors.In my answer, I mentioned something along the lines of using the 3-month LIBOR spot rate and 6-month LIBOR spot rate to compute the 3-month LIBOR rate 3 month forward.In today’s situation, this would not be correct and we will explore the reason below. A more appropriate example would be the use of US Treasury rates, where the lines of reasoning would hold and the relationship would look something like this:Relationship between spot and forward US Treasury ratesBefore going into the section on LIBOR curves, it is important to understand what are curves and their uses in pricing instruments. If you are familiar with the concept of curves, feel free to skip the first subsection.Pricing Instruments using CurvesAt the basic level, when we price an instrument with multiple cash flows (eg. fixed rate coupon…