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Let H be the barrier, S(max) be the maximum stock price and S(min) be the minimum price over the life of a European down-and-out put

Let H be the barrier, S(max) be the maximum stock price and S(min) be the minimum price over the life of a European down-and-out put option. What is its payoff function?
a.
max(K - S(T),0)xI with I = 1 if S(min) > H and I = 0 otherwise
b.
max(K - S(T),0)xI with I = 1 if S(max) < H and I = 0 otherwise
c.
max(K - S(T),0)xI with I = 1 if S(max) > H and I = 0 otherwise
d.
max(K - S(T),0)xI with I = 1 if S(min) < H and I = 0 otherwise
Let H be the barrier, S(max) be the maximum stock price and S(min) be the minimum price over the life of a European up-and-out put option. What is its payoff function?
a.
max(K - S(T),0)xI with I = 1 if S(max) > H and I = 0 otherwise
b.
max(K - S(T),0)xI with I = 1 if S(min) < H and I = 0 otherwise
c.
max(K - S(T),0)xI with I = 1 if S(min) > H and I = 0 otherwise
d.
max(K - S(T),0)xI with I = 1 if S(max) < H and I = 0 otherwise

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