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billyx524
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Posts: 32
Joined: February 12th, 2016, 4:48 pm

Pricing Down and Out Barrier Option by Replication

May 10th, 2017, 3:45 am

Hi,

I have been asked this question during a recent interview.  I was told this can be priced by a replicating strategy, but I have no idea how to do it.

Price an european call option.  Support current stock price is 100, with strike price 90, and down and out barrier at 90.  interest rate and dividends are zero.

How can I solve this by replication?

Thanks,
 
frolloos
Posts: 752
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

Re: Pricing Down and Out Barrier Option by Replication

June 2nd, 2017, 3:56 pm

You've heard of google? :) If you can't be bothered to search first, then at the very least post the question in the student forum. Anyway:

http://www.columbia.edu/~hz2244/teaching/Lec17.pdf

The crucial element is put-call symmetry. Generalizing it to non-homogeneous processes is hard, but I think your questions is in a Black-Scholes setting anyway.