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S(t) is the value of a share S at time t. A portfolio H consists of the following options on S(t) all with expiration T:

S(t) is the value of a share S at time t. A portfolio H consists of the following options on S(t) all with expiration T:

Long 1 call option struck at (K-a)

Short 2 call options struck at K

Long 1 call option struck at (K+a) where a

The payoff for this portfolio is the function P(S) = H(S(T)).

Work out the maximum value of P(S) and the share price which would achieve this maximum value.

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