Suppose that a stock price is currently $20 and that a call option with an exercise price
Problem 17.10.
Suppose that a stock price is currently $20 and that a call option with an exercise price of $25 is created synthetically using a continually changing position in the stock. Consider the following two scenarios:
a)Stock price increases steadily from $20 to $35 during the life of the option.
b)Stock price oscillates wildly, ending up at $35.
Which scenario would make the synthetically created option more expensive? Explain your answer.
Hint
The holding of the stock at any given time must be N(d1) . Hence the stock is bought just after the price has risen and sold just after the price has fallen. (This is the buy high sell low strategy referred to in the text.) In the first scenario the stock is continually bought. In second scenario the stock is bought, sold, bought again, sold again, etc. ...
The holding of the stock at any given time must be N(d1) . Hence the stock is bought just after the price has risen and sold just after the price has fallen. (This is the buy high sell low strategy referred to in the text.) In the first scenario the stock is continually bought. In second scenario the stock is bought, sold, bought again, sold again, etc.
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