How to value an interest rate swap

[NagaichPrateek]

Hi, thank you for the video. Quick question on the idea of pricing the legs.

When you price the fixed leg, you take into account all the future coupon payments and notional and then discount them. However, when you price the floating leg, you consider just one coupon and the notional. I may be understanding something incorrectly and I would appreciate if you could help me understand the concept behind the pricing of floating leg.

[NagaichPrateek]

@bionicturtlecom: I would really appreciate if you could show all of us the non-simplified form of calculating the price for floating leg and then simplify it confirming equivalence.

Thank You!!

[BlessedAgni]

Any chance you could share your excel files? Would be a great learning tool in addition to the videos. Thanks

[hemmu23]

@sammyjny.... the point is that the ISP is being valued in mid of the first leg of 6 months and hence if at that point of time want to know what am i getting i would need to take into account the fixed income part in toto while the payment in first leg that is floating leg is yet 3 months away and at 3 months form deal is what the example points to and hence the 3 month value of floating cupon is subtracted.... when we calculate at 0.5 yrs the value of ISP will be diff. hope some bit is clear...

[wanfight]

Hi, thank you sir for your kind explanation. I was wondering if you could please post something on accounting for derivatives?

[munit21]

first of all thanks for all your fantastic clips! saying that, my question is if you said that the floating rate that the coupon pays is the 6 month prior Libor rate, then how comes we did not use the 6 month rate that was applicable before time zero. i.e the 6 month rate that was just before the swap was agreed should be the correct rate that is to be used. is it not so?

[88sinduja]

Excellent vid. However, are we making an assumption by saying that LIBOR curve will remain fixed? How do we get around this assumption?

[88sinduja]

@88sinduja Actually I saw your previous comments on bootstrapping. Which makes sense I guess. Thanks for the vid, made things clear :-)

[andyv123]

Hi Bionictutle.

Firstly thank you for such a simple to understand tutorial on IRS. the only thing I don't understand is, by definition the variable leg of the swap is unknown, so how do you know what the swap rates should be? in your tutorial you made up those numbers, which means if i choose my own interest rate i can make the value of the swap to positive or negative.

[adaseth]

Did he say "Inception"? I must be in a dream, where's my totem, I knew they were trying to extract my bank account password! :P

[bionicturtledotcom]

@adaseth you have been in a dream the entire time: your totem is also unreal. We already have your account info :)

[edb1980]

@bionicturtledotcom I dont understand what you did with the exponential function rather then discount factor?

[sammyjny]

Thanks for your explanation. I understand the first part. However, I am still confused on the cash flows at the end of each term. Simply speaking why are you not looking at all the swap floating rate payments to get the net present floating leg value to determine the net credit/debit on the swap?

A related question is valuing the swap after the first settlement - do we only consider future payments in valuation from there on?

[bionicturtledotcom]

@sammyjny We you say is valid (of course) except it would give the same result. So it is merely a simplification that is possible only on the exact moment of settlement. When you asked why the bond isn't valued at par (100), that is the correct idea, at settle: our basis for determining future floating coupons is the forward rates and these necessarily reconcile with the discount rate. Similar to 100 * (1+r) / (1+r) = 100 but works for series of forwards.

...i'm not clear on your second part

[sammyjny]

ok i am completely confused how you priced the floating leg. First why you used the rate of 6 months divided by 2 and then discount it using 3 month... why not just use 3 month rate... in that case the present value will remain 100? Secondly, what happened to the floating rate payments at 0.75 and 1.25 time intervals ?

[bionicturtledotcom]

@sammyjny Future coupon pays LIBOR that prevailed at PRIOR 6 month settle (if LIBOR curve static, prior 6 mo L = 5.5%). But that's annual bond equivalent, so future coupon = 5.5%/2.

Discounting this $ to PV is next step, here disc. @ 3 mo. continuous. Your 100 par would be valid if 3 mo LIBOR = 6 mo LIBOR *and* coupon freq (semi-annual) = discount (continuous)

Re the 0.75 and 1.25 floaters: actually, this is where your idea applies: at settle, bond = par, so 100 effectively impounds them

[bionicturtledotcom]

@sammyjny ...(append) You've identified the two difficult ideas here:

1. Determination of (future) coupon cash flow is a function of the floating swap &, any time valuation is between coupon settlements, will differ from discount because the time horizon won't match (i.e., coupon is 6 month rate but discount is < 6 mo rate. Also, here the compound freq complicate)

2. At the future settlement exactly (here, +0.25 months), we do have a match. Then indeed discounted PV = par

[kldenis90]

Hey David, in an interest swap deal hull claims a fixed rate receiver is long the fixed rate bond and short the floating rate bond -- and the reverse is for the fixed rate payer. I am little confused by this construct because if the FR receiver is long the FR bond he/she is expecting interest rates to go down hence the increase in value of the FR bond (right?). But won't this be the same change in direction/value (i.e. an increase) for the FL rate bond since LIBOR would have gone down too.

[sweetsagit80]

thanks.. this is great

[broadex1]

Looks like a great presentation. But why are you using 5.5% for the floating rate which is the 6-months LIBOR after inception. I thought you are supposed to use a 6-month LIBOR at inception at day 0 and work out the interest to be paid at next coupon.

[nickia88]

How do you value these swaps in reality when the actual future LIBOR rate is unknown? Do you use the estimated LIBOR rate?

[100Explorer100]

@nickia88

I believe that you need to determine zero rates by a common bootstraping method, and then determine forward rates that are implied by current zero rates for periods of time in the future. I don't have enought space here to explain more in detail, though with some luck you may find some video about that. Just maybe talk to your professor about that in his/her office hours. Good luck

[dbullet]

Hello... anyone want to help me out and explain why we add the notional at the end of the period? We're valuing cash flows. It is my understanding that the notional is never excanged. Why not just discount the payments?

[Zapanath]

@dbullet the swaps are valued as if u were valuing a bond, the same principle.

[bigtimeglupek]

good job- 100% better than my idiot teacher's fucken 'phrase by phrase' power point

thank you

really good job

[rndllhllw]

Nice work. keep it up. mean time come for social media marketing for esteembpo**com

[okays123abc]

Great work

[kbabsjonah]

Hi this is a well explained video however, i just want to find out how you calculated the discount factors of 0.988,0.956

[sdkazmi]

he got 0.988 by dividing 1 by 1.0125. we get 1.0125 by dividing 5% which is annually by 4 since its for 3 months or quarterly. so 5% divided by 4 gives u 1.25 which again divided by 100 gives u 0.0125. add 1 to this and it will be 1.0125. divide 1 by 1.0125 and u get 0.9878.

[surferandre]

Hi, very good vid. I really like your stuff.

Just a quick question. Do you assume no change in LIBOR rates in the three months prior to the valuation date, or why do you use the CURRENT LIBOR/spot rate for the current floating coupon?

[sundisk]

Hi, which john hull's text are u using as reference for this example? Thanks

[kissjj803]

Excellent Video! Thank you.

Is this spreadsheet available for download? I'd like to see how you set it up. Thank you!

- Jessie

[soncheeba]

Hi Bionic, why/when do you used continuous versus annual compounding? In your example you are calculating the discount factor as df=exp(-rt), whilst other books tutorials etc would have used df = 1/ (1 + r )^ t. Thanks

[bionicturtledotcom]

Hi soncheeba, it could use discrete (annual) compounding instead. For my given continuous rate, there exists a higher annual rate that is equivalent. But continuous is more convenient/common in academic finance, is all. David

[100Explorer100]

@soncheeba

if I may, based on my academic knowledge continous compounding is a standard for valuation in derivative instruments- meaning: whatever compounding is given, you'd convert it into continuous for your own analysis purposes, and then back to whatever compounding for transaction purposes. I maybe mistaken, though. I think this is also the industry's practice to quote in continuous for some instruments, though it is a very good question I guess to Bionic

[kiepie85]

Why do you use 0.25,0.50,1.25 only and not 0.50 and 1.00.

And shouldn't 0.25 Cash flow be $2? Cause it is only a quater of an year.

[bionicturtledotcom]

It's a john hull example so .025, .50 is arbitrary: it's just to show pricing in-between coupons (T - 3 months to next coupon). Could be anything depending on T - ? to next coupon.

Cash flows are independent of discounting. First, get the cash flows. Second, discount them. And the cash flows are based on, fixed at 8% semi and floating, based on 6 month libor i.e. 1/2 of 5.5%