Suppose an option knocks in at H 1 > S, and knocks out at H 2 > H 1 . Suppose that K H 1

Suppose an option knocks in at H₁ > S, and knocks out at H₂ > H₁. Suppose that K 2 and the option expires at T. Call this a “knock-in, knock-out” option. Here is an equation summarizing the payoff to this option (note that because H₂ > H₁, it is not possible to hit H₂ without hitting H₁):

What is the value of this option?

if H not hit if Hi hit and H2 not hit if Hi hit and H2 hit Payoff = max(0. ST-K )