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My understanding is that in practice, off the run treasury bonds are priced using a spread to the on the run bonds.
How then are the on the run bonds priced - e.g. 5 year treasury?
If a discounting approach is taken, what are appropriate discount rates given this is risk free and there are few other instruments similar to it?
Treasury bonds are priced by supply and demand from investors. Probably the most important factor in pricing Treasury bonds is the expected path of short term interest rates over time. For example, the 5 year treasury yield is approximately equal to the average expected Federal funds rate in effect over the next 5 years. Many other factors come into play also, but that's the most important.
Unquestionably the most liquid point in interest rate markets is CME exchange-traded ten year note future. Because the basis between future and cheapest-to-deliver (CTD) bond cash price is relatively steady throughout the day, this provides a "knot" that determines the price of the belly of the curve.
Other "knots" may be from Fed Funds policy rate, and five/ten year benchmark cash bond prices. These bond prices are set according to supply and demand, for example, by E-Speed/BrokerTec digital exchanges. Market markers are given incentives to provide continuous liquidity on the exchange.
From these knots a cubic spline is used to generated a smooth Treasury yield curve - often new issue bonds or off-the-runs are priced as another basis to the splined curve rather than directly from current Treasuries.
As the market evolves, it may be that IRS provide more liquid knots than cash Treasury bonds due to the capital requirements of warehousing positions on balance sheet. In this case, we may in future see the 10y IRS become a driver of on-the run prices (e.g. 10y UST) as the swap-bond basis is similarly relatively steady.
