# Rate of return of a bond price

Assume $$B(t, T)$$ is a zero coupon bond price and assume that it has dynamics $$dB(t, T) = B(t, T)[\mu(t, T)dt + \sigma(t, T)dW_t]$$, where $$W_t$$ is a Brownian motion under $$(\Omega ;F; P)$$ and $$P$$ is an objective measure. We know that the functions $$\mu(t, T)$$ and $$\sigma(t, T)$$ are adapted processes. If $$Q$$ is a risk-neutral measure that is equivalent to $$P$$, how can I find the rate of return of the bond price $$B(t, T)$$ under $$Q$$?

• I am not too sure, but aren't the rate of return under risk-neural probability always risk-free rate under the Black Scholes' framework? – Preston Lui Nov 20 '20 at 3:21