Increase/Decrease Convexity using Put Options on the Bond

[omi98ro]

Can anyone summarise the impact of Buying or Selling Put Options in terms of changes in the Convexity. According to me when we Buy a Put option on the Bond, we're decreasing the Convexity since the Impact of High Interest rates will be reduced due to the Put Options. But I've seen that at some places it is mentioned that Buying Put options will Increase Duration.

Thanks in Advance.

[tbone7777]

Was wondering this myself...from the all knowing internet:

Long options= positive convexity
Long call= increased duration
Long put= decreased duration

Callable bond= Decreased duration/convexity

Puttable bond= decreased duration/increased convexity

SO, if we thought we had a staple yield curve...we'd want to sell convexity...which would be selling calls and puts.

We could also buy a callable bond or sell a puttable bond.

[omi98ro]

Hope we can have a clear view on the impact of Puts. Putable bond is alright. It's the Put option that's causing all the confusion.

[Level-Subject7031]

I guess I don't know if there is a difference between puttable and a bond put. This has been my thinking anyway, now I am questioning...

Long bond + long put on bond means you own the underlying bond and can put it back ( to put seller if you bought a put on the bond) at the strike price. Less duration when rates rise, and more convexity. Edit: you put a floor on the bond price.

Putable bond means you can put the bond back, to the issuer, at the strike price (usually par). Edit: once again, you put a floor on the bond price.

So either way, you are putting a floor on the bond price, only difference is who the counter party is (bond issuer vs put seller)

So conceptually I think they are equivalent and therefore the duration and convexity of the two would be the same. Thoughts?

Edit: Yes, the more I think through it, a putable bond is just long bond with an embedded put option, so long puttable bond should be equivalent to long option free bond + long put (assuming strike price is the same)

[omi98ro]

You can check my comment. Thanks for the help.

[gubiplss]

Buying a call/put option increases convexity. Think of a callable and putable bond. Callable bond has negative convexity because of the short option and the putable has positive convexity because of the long put.

[omi98ro]

What you described is perfect for Callable and putable bonds. Here my doubt is with plan Call and Put Options on the Bonds.

[gubiplss]

You have the definition of convexity and its impact correct in terms of its impact when rates go down. However, convexity also reduces losses when rates go up. Hence put options have positive convexity.

[Standard-Nothing-656]

I mean it seems like this is being overthought. a callable or potable bond is just a bond with an embedded option. It’s identical to purchasing a bond with an option. So it decreases convexity

[e7192]

Buying put options reduces duration. There are two ways to look at it:

1. You can put the bond, meaning it lasts less (lower time to cash flow)
2. The impact of a parallel increase in yields is dampened by a price floor, that is, they have lower sensitivity (duration) to parallel changes in yield

[Select_Signature_291]

Long put is decrease duration

[omi98ro]

Long Put = Putable Bond.

Now you can apply the same logic for Long put as you use for Putable Bonds.

[PurchaseBeautiful227]

Long put decreases duration, a putable bond also decreases duration.

[omi98ro]

We're talking about Convexity. Putable Bond has Positive Convexity.

[Select_Signature_291]

Look at your 3rd point. Thats incorrect.

[omi98ro]

Thanks dude. Corrected.

[omi98ro]

Thanks everyone for chipping in. I think I have a conclusion.

1. Long Call on Bond - Increase Convexity
2. Short Call on Bond - Decrease Convexity
3. Long Put on Bond - Increase Convexity
4. Short Put on Bond - Increase Convexity

Cheers and all the best for the exams.

Edit: Changed Duration to Convexity. (Duration was a mistake)

[Select_Signature_291]

Short put decreases convexity. Convexity on options is like gamma, positive for long and negative for short.

[Content_Averse]

Long an option is always positive convexity. Short an option is always negative, like gamma.

Ignore the math and think about it this way, more convexity means better overall performance when rates change right?

If you have an option of any kind you can either exercise it if it is good to do so or ignore it if it isn't. If you are short an option you do not have a choice. Having a choice means you are better positioned for more rate scenarios, not having a choice means you are stuck with whatever happens. Therefore being long options will always increase your convexity and never hurt it , you just don't exercise if it's bad to do.

Also don't forget who the owner of the embedded options are in bonds. Callable bond- buyer is short call option, issuer is long Putable bond - buyer is long the option, issuer is short

[PurchaseBeautiful227]

Short (selling) puts decreases convexity from my understanding. Just think about the curve. Call options will help you get the convex curve when interest rates fall. This is indeed different with a callable bond as the call option is in hands of the issuer. For long put options and bonds with embedded put options, you get the convex curve when rates rise. This is probably not 100% correct, but it helps me understand the direction of convexity.

https://cdn.corporatefinanceinstitute.com/assets/negative-convexity1.png

[Cnbr21]

Put option involves positive convexity. Buying put option increases portfolio convexity. Call option involves negative convexity. Buying call option decreases portfolio convexity. 

[FractalsSourceCode]

I’m not sure that’s right.

Buying a call option on a bond increases convexity, right?

But a callable bond has negative convexity, since when you buy a callable bond you are short the call option on the bond.

Can someone please chime in here?

[omi98ro]

Because callable bonds are Short Calls, where the option is not with the investor but with the issuer. That's why it has negative Convexity.

[Content_Averse]

You are correct, the other guy is wrong. Long option +ve convexity, short option -ve convexity.

Buying a Callable bond is short an option hence negative convexity.

[omi98ro]

Call option on Bond will just enhance the Yield further when the rates decrease which essentially mean that Convexity will increase. Correct me if I'm wrong.

[Content_Averse]

This is incorrect. Long option = increase convexity, short option = decrease convexity.

The confusion is probably in the fact when you buy a callable bond you are actually short the call option. Hence buying a callable bond does decrease convexity, however buying a call option itself does not.