Question

(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.

Answer 1

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. In the first scenario the stock is continually bought. In second scenario the stock is bought, sold, bought again, sold again, etc. The final holding is the same in both scenarios. The buy, sell, buy, sell... situation clearly leads to higher costs than the buy, buy, buy... situation. This problem emphasizes one disadvantage of creating options synthetically. Whereas the cost of an option that is purchased is known up front and depends on the forecasted volatility, the cost of an option that is created synthetically is not known up front and depends on the volatility actually encountered.