Would like to ask you, how would you price an Option which has its starting underlying price S0 = 70 dollars, with no dividends, and that pays 0.5 dollars each time the underlying price hits a barrier of 30 dollars.
Normally the initial Black Scholes PDE will be converted into a simpler ODE, has time decay = 0 (due to the perpetuity of the option).
How would you solve it\price it? (risk free rate is assumed to be constant)
I am mainly interested on the final pricing equation.