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Answer: The value of the option position has increased, but this increase is larger in magnitude than the decrease in value of the stock position used to establish the hedge.
## Explanation **A is correct.** In delta hedging a long call option position: - **Long call options have positive delta** (they gain value when the underlying stock price increases) - **Delta hedge requires short position in underlying shares** (negative delta) to offset the option's delta **Key issue:** The analyst miscalculated delta as 60,000 instead of the actual 70,000, meaning: - **Too few shares were shorted** (only enough for 60,000 delta instead of 70,000) - **Hedge is under-hedged** by 10,000 delta units **When stock price increases:** - **Option position value increases** (due to positive delta of 70,000) - **Short stock position value decreases** (due to negative delta of -60,000) **Result:** The actual gain from the option position (70,000 × price increase) is **larger in magnitude** than the loss from the short stock position (60,000 × price increase). **B, C, and D are incorrect:** - B is wrong because the option gain is larger, not smaller - C and D are wrong because the option position value increased, not decreased
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A manager at an OTC options dealer is reviewing the calculations of an analyst that were used to implement a delta hedge for a long position in a call option. The manager discovers that at the time the hedge was established, the analyst had estimated the delta of the option position as 60,000, but it was really 70,000. If the underlying stock has increased in price since the implementation of the hedge, which of the following statements is correct?
A
The value of the option position has increased, but this increase is larger in magnitude than the decrease in value of the stock position used to establish the hedge.
B
The value of the option position has increased, but this increase is smaller in magnitude than the decrease in value of the stock position used to establish the hedge.
C
The value of the option position has decreased, but this decrease is larger in magnitude than the increase in value of the stock position used to establish the hedge.
D
The value of the option position has decreased, but this decrease is smaller in magnitude than the increase in value of the stock position used to establish the hedge.
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