An eccentric client has walked into the prestigious o ces of Z-Bank asking for a quote on the following insurance contract. Under the terms of the contract, the "triggering event" occurs if the EBIT of Pegasus Corporation reaches the coupon on Pegasus Corporation debt. When and if the triggering event occurs, a neutral third party will ip a fair coin. If the coin comes up Heads, Z-Bank must pay the client $1 million. If the coin comes up Tails, the client must pay Z-Bank $1 million. What up-front price "H" would you charge this client assuming: the coin ip is fair in the sense that heads and tails are both equally probable; Pegasus Corporation EBIT will follow a standard geometric Brownian motion; and your boss values this client and so wants you to charge only a competitive price? Justify your answer using both verbal intuition and some math including boundary conditions on the relevant dierential equation.