Past exam of the martingales and financial mathematics course of the University of Oxford / 2007 / B / 8 / c / Solution

At maturity debt receives the smaller of face value and firm assets:Thus it is equivalent to a zero-coupon payment $F$ minus a European put option on the firm value. Its time-$t$ price isEquity receives the residual $(V_T-F{)}_{+}$, hence is a European call option:put-call parity verifies $E_t+D_t=V_t$, consistent with the stated balance-sheet identity. As with the replication arguments elsewhere, the physical drift $\mu$ does not enter these option prices.