Convexity of options in bonds

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shootforthestars1

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For callable bonds, when it’s call option is near the money (I presume in schweser language they mean At The Money, i.e. S = X), then its convexity turns negative! For putable bonds, convexity is always positive.
1. Can someone explain why convexity turns negative, i.e. the bond should gain more value when the coupon rate drops?
2. If it does turn negative, then what does the graph look like of convexity slightly away from ATM point? i.e. when exactly does it go from positive to negative to positive convexity again?
 
Yeap, read your article - it’s simple and helpful hammering what I know.
I’m just finding it difficult to digest that near ATM point for the call option, it’s convexity flips from positive to negative!
In your article it says, “however, there will be a point on the price/yield curve where it will start to curve downward;”
Why does Schweser chose the wordings “near the money point” ….?
 
As yield drops, the value of the option-free bond increases, and the value of the call option increases; furthermore, they both increase at an increasing rate. The inflection point (where the convexity is zero: it’s changing from positive to negative as the yield drops) occurs where the increase in the option value just matches the increase in the value of the option-free bond: for yields above that point, the value of the bond is increasing faster than the value of the option; below that point, the value of the option is increasing faster than the value of the bond.
It’s difficult to say exactly where the option is in the money or out of the money; it’s not like an option on a stock that has a specified strike price. Saying something like “near the money point” is just hedging based on that difficulty.
 
S2000magician wrote:
Saying something like “near the money point” is just hedging based on that difficulty.
Click to expand...
cool - that near the money thing had me confused. seems its not critical to nail down exactly where conv flips.
 
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