A barrier option is an option that changes its payoff when the underlying reaches certain price...

 

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A barrier option is an option that changes its payoff when the underlying reaches certain price levels or "hits a barrier." Consider a non-dividend-paying stock that has price 100 today, at Date 0. There is a barrier option X written on the stock. X has payoff defined as follows: it pays off the price of the stock the first time the stock hits the barrier of 1000 and nothing otherwise. In other words, if T is the first time that ST = 1000, then the XT = ST at T; at all other times t, X = 0. 1. What is the price Xo today, at Date 0? Explain briefly. If necessary, make and state any additional assumptions necessary for your answer. [10 marks] A barrier option is an option that changes its payoff when the underlying reaches certain price levels or "hits a barrier." Consider a non-dividend-paying stock that has price 100 today, at Date 0. There is a barrier option X written on the stock. X has payoff defined as follows: it pays off the price of the stock the first time the stock hits the barrier of 1000 and nothing otherwise. In other words, if T is the first time that ST = 1000, then the XT = ST at T; at all other times t, X = 0. 1. What is the price Xo today, at Date 0? Explain briefly. If necessary, make and state any additional assumptions necessary for your answer. [10 marks]

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To determine the price of the barrier option X at Date 0 we can use the concept of riskneutral valua... View the full answer