Pricing a barrier option from a binary option

[lukaluke]

Hi everyone,

I'm trying to understand the following question. Unfortunately I have not been abble to do so by now. Coul you help with it?

We consider a price process as follows:
dS_t = \sigma dW_t
with $S_0 = $100.
We know that the price of a binary put with strike $80 and which pays $1 if the underlying is below this strike at maturity is worth $0.35.
The question is to compute the price of a knock-out down-put with level at $80.

Thank you for your help. :D

 

[financeguy]

I'm going to assume "knock-out down-put" means "one touch", i.e. something which pays $1 if the underlying touches $80 at any point between today and maturity. Using the reflection principle, this is just twice the probability of the underlying finishing below this level. So the answer is 2*$0.35 = $0.70

 

[lukaluke]

Thank you.