2012 AM Q9B

Question in the exam: Determine whether the change in the price of the put option will be greater for an increase or decrease in the price of the underlying equity. Justify your response with one reason.

Answer: The change in the price of put options will be greater for an instantaneous decrease in the price of the underlying equity than for an instantaneous increase in the price of the underlying equity of equal size.

For put options, the delta will underestimate the price effect of decreases in the underlying equity and will overestimate the price effect of increases in the underlying equity. This is due to the convex relationship between put option prices and the price of the underlying equity. This can be addressed by adjusting the put option price for the effect of gamma, which is analogous to the convexity adjustment of a bond’s price.

I understand the answer, but I don’t think the explanation is relevant to the question. The official answer explains more on whether is the acutal option price will be higher/lower than the delta adjusted option price. But the question in the exam is aiming at the degree of price movement affected by the underlying price change.

I think the answer should be: as the underlying price decreases, the option will be more likely in the money. So the downward price change will have a larger impact on the option price movement.

I would have answered exactly what you have suggested.

Well, upon carefully examining…

_ change in the price of the put option will be greater for an increase or decrease in the price of the underlying equity _

The Qn is asking the option price sensitivity (greater) to change in price of the underlying (increase or decrease). And that whether the magnitude of sensitivity is greater for increase vs decrease. So I guess it refers to delta and gamma effects.

I am with you. After seeling so many "increase"s and "decrease"s, I would be quick to answer as you have

It is, actually.

The point is that the graph of the put’s price versus the underlying’s price is decreasing with positive convexity. Forget about delta and gamma and being in the money or out of the money and everything else that complicates this. The price graph is decreasing with positive convexity: a price increase of the underlying leads to a smaller price change (an increase) for the put than an equivalent price decrease in the underlying.

I have no idea what the distinction is that you’re making between the actual price change and the degree of price movement. They sound the same to me.

As a grader, I would not give you full credit for that answer. You’re coming at a simple answer very obliquely.

In short, when the answer is simple, give a simple answer.