When constructing a yield curve for derivatives purposes, what is the difference between cash and deposits rates?
My impression is that cash is a more generic term: deposits are a cash security, but so are US Treasury bills, commercial paper, repos, and so on, and each security has different yields. When you construct a yield curve, the short end is calibrated to a certain cash security.
When constructing a yield curve of, for example IBOR rates, there is often a misunderstanding between floating rates (or the input to the curve that can control the floating rates) and the published IBOR rates, which impact the pricing of Interest Rate Swap derivatives. The nomenclature of these can change but on my desk we called them "deposit rates" or "cash rates" for those that controlled the floating LIBOR rates and "LIBOR rates" for the actual day's published fixings. On our desk "cash" and "depo" rates were the same thing.
Let me give you an example:
Its 9am and you are pricing a spot-2Y 6M-LIBOR Interest Rate Swap. You don't know what the 6M LIBOR fixing for the day is yet so you have a guess, say 1%, and you set both your 6M deposit rate input and your 6M LIBOR rate to 1%. Then you price the swap as usual.
Shortly passed 11am the LIBOR fixing is released at 1.005%, you consider this a little bit high and keep your 6M deposit rate marked at 1% (this controls what your forward curve expects tomorrow and the next day etc.), but your 2Y IRS is now updated to use the actual LIBOR fixing.
At 12pm the Bank of England cut rates by 25bp. The 6M LIBOR fixing for tomorrow is now expected at 0.9% so you have to set the deposit rate on your curve to around 0.9% in order to control it, but of course todays LIBOR was published at 1.005% so you must recognise that as a distinct rate.