How to value an interest rate swap

At inception, the value of the swap is zero or nearly zero. Subsequently, the value of the swap will differ from zero. Under this approach, we simply treat the swap as two bonds: a fixed-coupon bond and a floating-coupon bond. The value of the swap is difference between the two.

Category:

Education

Tags:

• Finance
• derivatives
• interest
• rate
• swaps

[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 :)

[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 ...(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

[edb1980]

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

[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!!

[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.

[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]

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

[88sinduja]

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