View Full Version : question about cap and floor

yueZHAO

03-25-2008, 10:15 PM

cap can be recognized as a put option. does it right?

if so, why calculate caplet value using the b-s model for call?

:exams: :oops:

:danim:

Laurelinda

03-26-2008, 12:03 AM

I think of a cap as being short a call: If the interest rate (or whatever security) rises above the strike, you lose the difference. (If you were long a call you would gain the difference.)

I haven't seen a cap treated as a put before. It doesn't quite make sense to me because a put option is the right to sell something at a good (high) price, so it's activated when the price falls. A cap only pertains to when the security rises. Does that make sense? Do you have a reference (book, page number)?

Car'a'carn

03-26-2008, 12:04 AM

What is a cap? What is the payoff of a put? call?

yueZHAO

03-26-2008, 01:55 AM

Thanks, Laurelinda.

2003 C8V: Question #23 (a)

I think the anwser is not right. do you agree with me?

Laurelinda

03-26-2008, 11:09 AM

2003 C8V: Question #23 (a)

Ah, I see. I took a look, and I think I've missed something. :oyh:

When we're thinking of an interest rate caplet as a call, it's a call on interest rates.

When you think of an interest rate cap as a put (or portfolio of puts), it's a put on bond prices.

The strikes are different, the reference security is different, and interest rates and bond prices move in opposite directions.

See the Hull chapter on Interest Rate Derivatives. (I have an old edition in front of me at work, so I'm not sure what the chapter number is in the new edition.) Look for the section entitled "Interest Rate Caps" and the subsection "A Cap as a Portfolio of Bond Options". You'll see the payoff formula mentioned in the exam question. Under "Valuation of Caps and Floors", you'll notice that the payoff looks different.

Tangential question...this section wasn't on the syllabus this year, was it?? Because I totally missed it.

The Smokin' Cracktuary

03-26-2008, 12:16 PM

Ah, I see. I took a look, and I think I've missed something. :oyh:

When we're thinking of an interest rate caplet as a call, it's a call on interest rates.

When you think of an interest rate cap as a put (or portfolio of puts), it's a put on bond prices.

The strikes are different, the reference security is different, and interest rates and bond prices move in opposite directions.

See the Hull chapter on Interest Rate Derivatives. (I have an old edition in front of me at work, so I'm not sure what the chapter number is in the new edition.) Look for the section entitled "Interest Rate Caps" and the subsection "A Cap as a Portfolio of Bond Options". You'll see the payoff formula mentioned in the exam question. Under "Valuation of Caps and Floors", you'll notice that the payoff looks different.

Tangential question...this section wasn't on the syllabus this year, was it?? Because I totally missed it.

I believe this is correct. I am sorry if this is a bit jumbled and somewhat innacurate, it's been a few weeks since I read this.

There is that section for different choices of numeraire to change something into a martingale. To use Blacks model you the underlying price must be a martingale, and must be a price (interest rates are not prices). So, I believe when modeling interest rate derivatives with B-S, the price of a zero coupon bond is the numeriare, essentially translating the price change in a zero coupon bond into a change in interest rates that follows a martingale via the lognormal distribution underlying B-S.

So, it is correct to say that a caplette is a put option on the price of a zero coupon bond as it moves inversely with interest rates (i.e. call on interest rates = put on price of a zero).

I may not be applying the whole idea of a numeraire here correctly, but it's something like that. Feel free to correct me. Again, I read it a few weeks ago. I am really just voicing this as much for my own benefit. I also don't exaclty remember which one is a cap and which one is a floor, so I may have something reversed above, but the idea is valid.

But I am sure that that is why it is a priced as a call option on the bond price. All blacks models work by assuming a price change has a lognormal distribution going forward, hence the underlying variable must be a price.

And I am pretty sure this is all on the syllabus.

yueZHAO

03-26-2008, 10:07 PM

Great. Linking this chapter with others that relative to collar, I understand it better.

To Laurelinda, "Hull chapter on Interest Rate Derivatives" is not on the syllabus. Also, you must be a expertise, or shall be. Thanks.

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