Perpetual derivative f. Consider a financial derivative paying a fixed amount Q whenever the underlying price S reaches the level H for the first time. To price this derivative follow the next steps: (a) Noticing that a perpetual derivative means it does not depend on time, write the corresponding Black-Scholes Merton PDE (b) Consider first the case where SH : i. What are the boundary conditions in this scenario? ii. Since a linear function no longer works, define f as a power function (with power parameter ) joining the boundary points and obtain the value of replacing in the Black-Scholes-Merton PDE. (d) If S=100,H=98,Q=5,T=1,r=0.05 and =0.2, what is the price of the perpetual derivative