Why is bond option convexity asymmetric?

CFA Level III
#1

Reading 24 CFAI Text section 3.2.2 buying convexity - can someone explain why the dotted curve in Exhibit 11 is for option value prior to expiration?

(2) Why is convexity asymmetric for an option on a bond?

(3) Also why is it that when you want to increase convexity, you buy call/put, and when you want to decrease convexity, you sell a call/put?

Thanks!

#2

Exhibit 11 portrays the payoff on a call option and the value of a call option prior to expiration; the asymmetry is in the payoff, not in the convexity.

It’s the same sort of payoff diagram you had at Level I, and at Level II, and in Applications of Derivatives at Level III.

Puts and calls have positive convexity: the price graphs curve upward (as illustrated in Exhibit 11 for a call option). If you buy more, you get more positive convexity; if you sell more, you get less positive convexity.

#3

Thanks, I understand the value of a call option but I’m just not wrapping my head around the dotted curve (why it doesn’t coincide with the solid line for value of the call at expiration). Sounds like a refresher is needed for level 1/2…

#4

The dotted line represents the option’s value prior to expiration, which includes both intrinsic value and time value.