(No-arbitrage derivation of bond-pricing equation). In Section 6.5, we began with the stochastic differential equation (6.5.1) for the interest rate under the risk-neutral measure $\widetilde{\mathbb{P}}$, used the risk-neutral pricing formula (6.5.3) to consider a zero-coupon bond maturing at time $T$ whose price $B(t, T)$ at time $t$ before maturity is a function $f(t, R(t))$ of the time and the interest rate, and derived the partial differential equation (6.5.4) for the function $f(t, r)$. In this exercise, we show how to derive this partial differential equation from no-arbitrage considerations rather than by using the risk-neutral pricing formula.