Need help with understanding delta - put options price change vs U/L price change - underestimate vs overestimate

CFA Level III
#1

It came from 2012 AM:

The change in put price for decrease in U/L price > change in put price for an increase in U/L price of equal size

  • OK…I take it as a fact. That means when U/L price goes down, the put price will go up in a greater degree than it will go down when U/L price goes up.

Somehow the following is the most confusing part, and I just can’t wrap my head around this:

Delta will underestimate the price effect of decreases in U/L, and overestimate the price effect of increases in U/L

-Uh?? Since the decrease in U/L causes a greater movement in put price, how come it will underestimate the decreases in U/L?

#2

Suppose that the delta is −0.3 and the price of the underlying decreases by $10. Delta suggests that the option price will increase by $3.00 (= −0.3 × (−$10)), but it will in fact increase by more than $3.00: maybe $5.59. So you underestimated the price change.

Suppose that the delta is −0.3 and the price of the underlying increases by $10. Delta suggests that the option price will decrease by $3.00 (= −0.3 × $10), but it will in fact decrease by less than $3.00: maybe $1.48. So you overestimated the price change.

#3

Ah…so they were actually talking about the actual option prices vs the implied prices from delta…Thanks a lot Magician!

#4

You’re welcome.

#5

Also, they show the convexity of a call, but pretty much draw Option value on Y and X has underlying, make it convex. Delta is linear. So you can see the adjustments.