Yield curve - Embedded Options - Allardyce

S

Snah

New member
Joined
Jun 18, 2026
Messages
0
Reaction score
0
Hi,
All else being equal, as the yield curve flattens, the value of the call option embedded in Bond A increases. Thus, although the value of Bond A increases, the increase is partially offset by the increase in the value of the call option. Therefore, Bond A does not increase as much as the straight bond. As the yield curve flattens, the value of the put option embedded in Bond B declines because opportunities for the investor to put the bond decline. Bond B will increase as the yield curve declines but not as much as the straight bond.
That statement contradicts the 45.e LOS which says that callable and putable bonds will decline in value when an up-ward sloping yield curve flattens.
I though both declines because in the case of the putable the put option loses more value than the bond and viceversa with the callable.
Some insights?
Thanks
S
 
hey,
I think youre wrong about 45.e. The higher the back end of the curve, the more likely you as investor are losing money on your bond, so the more valuable is your put on the bond.
My interpretation is
call has less chance of being exercised with steep curve ==> callable bond being bond -call is more valuable
put has more chance of being exercised with a steep curve ==> putable bond being bond + put is more valuable
I hope it helps.
Also, Im stock on a different topic. would appreciate if you could share your thoughts if you get a chance:
http://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/91351705
 
I dont get your interpretation mate
 
int rate goes up, your bond (you being investor) is less valuable. if the bond is putable, that optionality is very valuable since you can sell the bond at strike. this upside from your put option partially cancells the drop in value of the putable bond.
This is not the case for a callable bond as your short the option (i.e. the issuer has the option to call back to the bond) hence the partial cancellaiton is not there. ==> you expect to lose more with a callable bond compared to a putable bond.
reverse happens with flattening..
 
But that depends of what parte of the ecuation changes more; in your example value of the put goes up but the value of the straight bond goes down; my question is which part is stronger?
 
I have trouble understanding this questin too. The explanation for number4 “ As the yield curve flattens, the value of the put option embedded in Bond B declines because opportunities for the investor to put the bond decline. Bond B will increase as the yield curve declines but not as much as the straight bond.”
Putable bonds=Straight+Put option. Even thought put option value decreases as the yield curve flattens, the putable bonds value will still be at lease equal or greater than the straight bond since it adds an additional “put option value”. Why the putable bond B increaes not as much as the straight bond?
 
This is how it is in my mind:
As to which part is stronger, think of it as:
Change in Value of the Bond(Price) > Change in Value of the Option
That is why when in a normal case of: “Int rates increase leads to Bond Price decrease”, the “Bond Price decrease” will be cushioned by the opposite effect on Price by Change in Option Value (and vice versa when interest rates decline).
The change in option value can be +ve or -ve but its effect on Price will be to counteract the original effect of Int rates on Price of Bond. In detail:
Demonstrating that when interest rates decline, both call and put options lead to decrease in Bond Price:
Interest rates decline —> Bond Price Increases —-> Call option value increases (which decreases Bond Price but in a lesser way than Bond Price increases) — > Net Effect = Price rise but not as much as straight
Interest rates decline —> Bond Price Increases —-> Put option value decreases (which decreases Bond Price but in a lesser way than Bond Price increases) — > Net Effect = Price rise but not as much as straight
Demonstrating that when interest rates rise, both call and put options lead to increase in Bond Price:
Interest rates rise —> Bond Price Decreases —-> Call option value decreases (which increases Bond Price but in a lesser way than Bond Price decreases) — > Net Effect = Price falls but not as much as straight
Interest rates rise —> Bond Price Decreases —-> Put option value increases (which increases Bond Price but in a lesser way than Bond Price decreases) — > Net Effect = Price falls but not as much as straight
 
I guess the key to this question is “changing more rapidly”. What they asked is the “percentage change”.
 
value of straight bond rises
value of straight bond rises, offset by an increase in the issuers call option
value of straight bond rises, offset by a decrease in the investors put option
 
olympria wrote:
This is how it is in my mind:
As to which part is stronger, think of it as:
Change in Value of the Bond(Price) > Change in Value of the Option
That is why when in a normal case of: “Int rates increase leads to Bond Price decrease”, the “Bond Price decrease” will be cushioned by the opposite effect on Price by Change in Option Value (and vice versa when interest rates decline).
The change in option value can be +ve or -ve but its effect on Price will be to counteract the original effect of Int rates on Price of Bond. In detail:
Demonstrating that when interest rates decline, both call and put options lead to decrease in Bond Price:
Interest rates decline —> Bond Price Increases —-> Call option value increases (which decreases Bond Price but in a lesser way than Bond Price increases) — > Net Effect = Price rise but not as much as straight
Interest rates decline —> Bond Price Increases —-> Put option value decreases (which decreases Bond Price but in a lesser way than Bond Price increases) — > Net Effect = Price rise but not as much as straight
Demonstrating that when interest rates rise, both call and put options lead to increase in Bond Price:
Interest rates rise —> Bond Price Decreases —-> Call option value decreases (which increases Bond Price but in a lesser way than Bond Price decreases) — > Net Effect = Price falls but not as much as straight
Interest rates rise —> Bond Price Decreases —-> Put option value increases (which increases Bond Price but in a lesser way than Bond Price decreases) — > Net Effect = Price falls but not as much as straight
Click to expand...
So in all the cases will be always “not as much as straight”
 
You must log in or register to reply here.
Back
Top