# Boundry Condutions

Any tricks to remember the Option’s Boundry Condutions for US and EU Options??

haha you know i’m scared to open any posts with qns by you esp at this moment…i feel so demoralized if i dont know how to ans it…i need motivation

This is how I try to remember. (notation note: rfr = (1+rfr)T) Calls pay max(0, S-X), puts pay max(0, X-S) Calls are the same C - max(0, S-X/rfr) S Puts are the same except the factor of rfr for European EP - max(0, X/rfr-S) X/rfr AP - max(0, X-S) X

thats exactly how i remember it… Calls are the same… Puts are different, due to the fact that EURO’s can only be exercised at maturity, thus you have to PV the exercise price… AND it helps me to visualise the payoff diagrams too… just in terms or working out if its (X-S) or (S-X)

‘calls aren’t the same’ for euro calls though if i understand it right…? call euro = max(0, S-X/(1+r)t)

The “boundary conditions” for American and European calls (not US and EU) aren’t really very important for the curriculum. They are needed for solving the B-S differential equation. For a call they are: At expiration, if S = 0, Call Value = 0. and as s -> Infinity, Call Value/(S-X) -> 1. Similar for a put. I wouldn’t worry about this at all.