Problem bank
Problem 305 of 333MediumStochastic ProcessesP305
Did the take-profit ever get touched?
A stock trades in 1-cent ticks, and each tick is up or down with probability , independently. You buy at the open and leave a sell limit order 3 cents above your entry price. Treat the order as filled the first time the price touches that level.
(a) After 10 ticks the price is exactly back at your entry. What is the probability that the price touched your limit level at some point during those 10 ticks?
(b) Without knowing where the price ended, what is the probability the order was filled within the 10 ticks?
See the hint and solution with a free account
Every problem on Quant Engine is free, with a hint and a full worked solution. Making an account takes 30 seconds and no card. Then you can see them and track what you have solved.