hello,say the spot is 38.5, risk free rate at 2%, no divs, spot vol at 20% and the down and out 3-month 38 call (european in nature) is trading at 0.40.Can it trader under intrinsic ?rds,

sounds like the knockout probability is quite high

how can I convince someone then that it's not an arb ?

so you have a pricing model ?

no, are there any model-independent truths here?he thinks it's impossible for it to go below intrinsic.basically, the knockout probability, independently of any model, should be monotone increasing with volatility, right?If vol is high enough, over the next infinitesimal time, you tend to proba knockout=1 and in that case the down and out should be worth 0, which is less than intrinsic.Is this arg valid?

the barrir is only 1.3% away from spot - the model would think that there is a high probability of touching it. Ask him how much the down-and-in call is worth ?

there is no down and in.he says because he can buy the down and out under "intrinsic", and sell spot, he can arb it. what ever happens he locks in a profit.looks right.scenario 1: never knocks out. ie, spot stays above 38 all the time. if it ends at 38, he loses 0.4 on the call and makes 0.5 on short spot, netting 0.1 at 38.1, he loses 0.3 on the call and makes 0.4 on short spot netting 0.1 at 39, he makes 0.6 on the call and loses 0.5 on short spot netting 0.1scenario 2: knocks out, it spot goes < 38. As soon as that happens, he closes his short, loses 0.4 on call and makes 0.5 on spot.so in all scenari, he makes 0.1 (ignoring cost of carrying short spot if any). so the minimum call price has to be instrinsic with cost of carrying adjust

correct?

this barrier is continuous monitoring.the doubt i have is whether the fact that he needs to be monitoring the barrier continuously to close his short nullify it.

this is correct. the theoretical price is around 52c and the delta is slightly > 100.