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The probability that a European call option will be exercised (S T > X) in a risk-neutral world isN(d 2 ). What is an expression

The probability that a European call option will be exercised (ST > X) in a risk-neutral world isN(d2). What is an expression for the value of a derivative that pays off $100 if the price of a stock at timeTis greater thanX, and $0 otherwise? Please explain.

(The discount factor ise-rT)

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