CA Final Strategic Financial Management, Paper 2, Chapter 5

CA .Tarun Mahajan

Swaps basic

Valuation of swap

Swaption

Interest rate forwards

Caps, floors & collars

It is a bunch of forward contracts.

Here cash flows are exchanged periodically according to a predefined formula.

In an interest rate swap one party agrees to pay fixed interest and other party pays floating interest on a notional principal.

For example I will pay you 8% p.a. on Rs.100cr. for next 5 years and you will pay me SBI-PLR.

Generic swap means a swap where the floating rate is LIBOR. It is also named

as plain vanilla swap. In a generic swap fixed payment is based on 30/360 days convention, i.e., assuming 30 days in a month and 360 days in a year. Floating rate payment is calculated on actual/360 days.

Actual/360 days is named as money market convention while actual/365 is called bond equivalent.

Non generic swap: all the swaps other than generic swap. For example: Libor

vs prime rate, deferred swap, swaption etc.

Overnight Index Swap is an interest rate swap involving the overnight

rate being exchanged for some fixed interest rate.

All in cost swap means a swap in which rates are quoted in such a

manner that it includes transaction cost and service charges also. Means no charges are levied separately.

Suppose a swap dealer quotes an all is swap as Libor vs. 5.9/6.1.

It means that dealer will pay 5.9% p.a. fixed in return for Libor.

And will pay Libor in return for 6.1% p.a. fixed.

Swap Dealer

6.1% 5.9%

Libor Libor

To make valuation of a swap we can divide it into two parts:

A bond paying fixed coupon and A Variable rate note.

Now we can calculate present value of both bonds. Difference in their value will be the value of swap.

Mostly swaps have zero value at inception, though there may be non par swaps also.

In a swap A will B 6% p.a. fixed, while B will pay Libor for next three year, at the end of each year.

If Libor is expected to be 5%, 6% & 8% and YTM for a 3 years bond is 6% then:

Value of variable coupon bond =

( ) ( ) ( )1 2 25 6 8+100100.74 = + +

1.06 1.06 1.06

Value of fixed rate bond is Rs.100 because YTM is equal to coupon.

For a fixed rate payer value of bond = 100.74-100 = Rs.0.74

While for a fixed rate receiver it is -0.74.

It is an option to enter into swap.

A 3 months into 5 years swaption means option

to enter into 5 years swap after 3 months.

A call option would be the right to enter into swap as a fixed rate

payer.

If the strike rate is 6% and actual fixed rate

after 3 months happens to be 7% then holder

will exercise his option.

A put option would be the right to enter into swap as a fixed rate receiver. If market rate falls then holder will exercise his option.

If direction of interest rate is predictable then one can enter into swaps to convert from floating to fixed or vice versa.

But if direction is uncertain then one can use swaption for the same.

Rate at which money is lent/borrowed as of today is called Spot rate.

S3 means the rate of interest for a 3 years loan as of today.

Contract to borrow/lend money in future is called forward contract and the relevant rate is called forward rate.

1f2 means rate of interest for a one year loan to be taken 2 years from now.

Spot rate is equal to geometric mean of forward rates.

1f0 = 10%, 1f1 = 11%, 1f2 = 12%, calculate S3.

S3= [(1+ 1f0) x (1+ 1f1) x (1+ 1f2) ]1/3 - 1

S3= [1.10 x1.11 x1.12 ]1/3 - 1= 11%

A shortcut would be to take arithmetic Mean instead of geometric mean.

S2 = 10.5%, S3 = 11%, Calculate 1f1. 1f2 = (1.11)3/(1.105)2 - 1 = 12% A shortcut would be 1f2 = S3x3 S2x2 = 11x3-

10.5x2 = 12%

( )( )

33

1 2 22

1+Sf = -1

1+S

YTM is the single rate at which present value of payment to bondholders becomes equal to current price of bond.

While spot rate is the rate which can be used to calculate present value of cash flow of a single point of time.

If YTM for different maturity bonds is given then we can calculate spot rates as follows:

6 months Spot rate = 8%

It is same as 6 months YTM because there is only one payment for the 6 month Bond.

1 year Spot Rate:

50/(1.04) + 1050/(1+S/2)2 = 1000; S = 10.05%

18 months Spot Rate:

60/(1.04) + 60/(1.05025)2+ 1060/(1+S/2)3 = 1000; S = 12.17%

Details of three semiannual coupon bonds

Bond Maturity Coupon YTM Price A 6 months 8% 8% 1000 B 12 months 10% 10% 1000 C 18 months 12% 12% 1000

Cap: It is a series of interest rate call options.

It is used by floating rate borrowers to hedge the risk of increase in interest rate.

When interest rate increases. On one hand borrower has to pay higher interest but on other hand it gain by exercising the call

Each option in cap is called the caplet.

Borrowed amount $1 million @Libor, payable quarterly. Cap @ 6%.

Quarter Libor Interest Cap Net

After hedging with cap interest outflow is never more than $15000

1 7% -17500 +2500 -15000 2 5% -12500 - -12500 3 8% -20000 +5000 -15000 4 4% -10000 - -10000

Floor: It is a series of interest rate put options.

Used by floating rate lender to hedge the risk of downfall in interest rate. Or

Floating rate borrowers also use it to defray some of the cost of a cap by taking a short position in floor.

When interest rate decreases below strike price then the short floor will have to make a payment

Each option in a floor is called the floorlet.

Interest rate Collar is combination of the long cap & short floor.

It is created by floating rate borrower to make cost effective hedging.

Long cap gives protection against rise in interest rate &

Short floor reduces cost of hedging (by sacrificing benefit of lower interest rate)

Interest rate can also be used as an underlying for derivatives

IRS can be used to convert fixed to floating rate and vice versa

Swaption are option on swap

Spot rate is geometric mean of forward rates

Collar is cost free hedging option

CA. Tarun Mahajan tarunmahajanca@gmail.com

SwapsLearning ObjectivesSwaps: IntroductionSwap: TerminologiesSwaps: terminologiesSwaps: ExampleSwap: ValuationSwap: Valuation ExampleExample continued..SwaptionSwaption continued..Interest Rate DerivativesForward Interest ContractDeriving Spot Rate from Forward RateDeriving Forward Rate from Spot RatesBootstrapping: YTM to Spot RatesExampleCapsExampleFloorsCollarLesson SummaryThank you