How can you utilize the traded prices

Question

How can you utilize the traded prices?

Answer 1

Imagine that you live inside a world where interest rates change in a fully deterministic way, no randomness at all. Here interest rates may be low now, but increases in the future, for illustration. The spot interest rate is the interest you obtain from one instant to the next. During this deterministic interest-rate world such spot rate can be written as a function of time, r(t). When you knew what this function was you would be capable to value fixed-coupon bonds of each maturity using the discount factor

Here to present value a payment at time T to today, t.
And deterministic spot rate function, r(t).