Consider a discretely monitored down-and-out call option with strike price X and barrier level B i at

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Consider a discretely monitored down-and-out call option with strike price X and barrier level Bi at discrete time ti,i = 1, 2, ··· ,n. Show that the price of this European barrier call option is given by (Heynen and Kat, 1996)

Cdo (So, T; X, B, B2,... , Bn) = So Nn+1(d, d,..., dn+; I) - e-Ti -rT N+1(d, d, ..., d+; r),where

In+(+) o ti d=d - 0, i = 1, 2, ..., n, In +(+)T dn+ = d+-oT. ONT Also, I is the (n + 1)  (n + 1) correlation

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