TOPIC****Finance:::::BLACK-SCHOLES model (solution of bond price equation)******

Ques***Show that the equation for the bond price has the explicit solution

.

Where r(t) is the risk-free interest rate, K(t) is the dividend payment, V(T)=F. Also,

if the interest rate r is constant, show that

Ques***Show that the equation for the bond price dtdV=r(t)VK(t) has the explicit solution V(t)=etTr(s)ds[F+tTK(y)eyTr(s)dsdy] Where r(t) is the risk-free interest rate, K(t) is the dividend payment, V(T)=F. Also, if the interest rate r is constant, show that V(t)=Fer(Tt)+tTK(y)er(yt)dy Ques***Show that the equation for the bond price dtdV=r(t)VK(t) has the explicit solution V(t)=etTr(s)ds[F+tTK(y)eyTr(s)dsdy] Where r(t) is the risk-free interest rate, K(t) is the dividend payment, V(T)=F. Also, if the interest rate r is constant, show that V(t)=Fer(Tt)+tTK(y)er(yt)dy