1. Financial Innovations and Product Design II
Products and Markets
Financial Innovations and Product Design II
Financial Innovations and Product Design II

2. Measuring Interest Rates
Compounding m-times per annum (annual, semiannual, quarterly etc.):
Continuous compounding: mn R m
A 1 +
eRn
Financial Innovations and Product Design II

3. Measuring Interest Rates
Conversion formulas:
Rc : continuously compounded rate
Rm: same rate with compounding m times per year
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4. Financial Innovations and Product Design II
Interest Rate Markets
Types of rates
Treasury Rate
Applicable to borrowing by a government in its own currency
LIBOR
London InterBank Offer Rate
Interest rates charged in trading between banks
Repo Rate
Sale and repurchase at a slightly higher price
Most common: overnight repos
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5. Financial Innovations and Product Design II
Interest Rate Markets
Zero Rates:
Zero-coupon rate
The n-year ZR is the rate of interest earned on an investment that starts today and lasts for n years with no cash flows in between
Also referred to as the n-year spot rate
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6. Financial Innovations and Product Design II
Interest Rate Markets
Bond pricing:
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7. Financial Innovations and Product Design II
Interest Rate Markets
Bond pricing:
Using zero rates:
Using bond yields:
Bond yields are bond specific!
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8. Financial Innovations and Product Design II
Interest Rate Markets
Par Yield:
The par yield for a certain maturity is the coupon rate that causes the bond price to equal its face value
Example using zero rates from the previous example solves
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9. Financial Innovations and Product Design II
Interest Rate Markets
Bootstrap Method:
A method to extract the zero rates from prices of instruments that trade
Bond
Time to
Annual
Bond
Principal
Maturity
Coupon
Price
(dollars)
(years)
(dollars)
(dollars)
Zero rates
Three-month:
Six-month:
1 year:
10,127%
10,469%
10,536%
100
0.25
97.5
100
0.50
94.9
100
1.00
90.0
100
1.50 8
96.0
100
2.00 12
101.6
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10. Financial Innovations and Product Design II
Interest Rate Markets
Bootstrap Method:
1,5 year zero rate?
Solution yields R = 10,681%
Calculation of the 2 year zero rate is similar, R = 10,808%
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11. Financial Innovations and Product Design II
Interest Rate Markets
Forward rates:
Future zero rates implied by the current term structure of interest rates
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12. Financial Innovations and Product Design II
Interest Rate Markets
Forward rates:
Future zero rates implied by the current term structure of interest rates
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13. Financial Innovations and Product Design II
Interest Rate Markets
Forward rate agreement:
OTC agreement that a certain interest rate will apply to a certain principal during a specified future period of time
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14. Financial Innovations and Product Design II
Interest Rate Markets
Term structure theories:
What determines the shape of the zero curve?
Expectations theory: long-term interest rates reflect expected future short-term interest rates
Segmentation theory: no relationship between short-, medium- and long-term interest rates
Liquidity preference theory: forward rates should always be higher than expected future zero rates
Financial Innovations and Product Design II

15. Interest Rate Markets Day count conventions:
Define the way interest accrues over time
Interest earned between two dates:
Actual/actual: used for Treasury bonds
30/360: used for corporate and municipal bonds
Actual/360: used for T-bills and other money market instruments
Number of days between dates
Number of days in reference period
x Interest earned in reference period
Financial Innovations and Product Design II

16. Interest Rate Markets Quotations: Bonds:
Quoted price is for a bond with a face value of 100
Quoted in dollars and thirty-seconds of a dollar:
Example:
quoted price: /32 = 90,15625
The price paid by the purchaser: cash price:
Cash price = Quoted price + Accrued interest since last coupon date
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17. Financial Innovations and Product Design II
Interest Rate Markets
Quotations:
Treasury Bills:
If Y is the cash price of a T-Bill that has n days to maturity, the quoted price (discount rate) is:
This discount rate is not the same as the rate of return earned on the T-Bill – dollar return/cost
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18. Financial Innovations and Product Design II
Interest Rate Markets
Treasury bond futures:
Long-term interest rate futures contract
Any government bond that has more than 15 years to maturity on the first day of the delivery month and that is not callable within 15 years from that day can be delivered.
Because any bond that satisfies the conditions can be delivered, a parameter called „conversion factor“ is applied to obtain the price received by the party with the short position.
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19. Financial Innovations and Product Design II
Interest Rate Markets
Treasury bond futures:
The cash received then equals:
Conversion factor:
It is approximately equal to the value of the bond on the assumption that the yield curve is flat at 6% with semiannual compounding
Cheapest-to-deliver bond:
Since many bonds can be delivered, the CTD bond will be the one that ensured that following quation is minimized:
(Quoted futures price x Conversion factor) + Accrued interest
Quoted price – (Quoted futures price x Conversion factor)
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20. Financial Innovations and Product Design II
Interest Rate Markets
Treasury bond futures:
Wild card play:
Taking advantage of different trading times in the T-bond futures market and the T-bond spot market.
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21. Financial Innovations and Product Design II
Interest Rate Markets
Eurodollar futures:
Eurodollar: a dollar deposited in a U.S. or foreign bank outside the U.S.
Eurodollar interest rate: the rate earned on Eurodollars deposited by one bank with another bank
Three-month ED futures contracts are futures on the three-month ED interest rate, they have maturities in March, June, Sept., Dec. For up to 10 years in the future.
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22. Financial Innovations and Product Design II
Interest Rate Markets
Eurodollar futures:
If Q is the quoted price for a EDF contract, the value of the contract is given by:
Q is set so that on delivery day Q = 1 – R, where R is the 3 month ED interest rate on that day.
10.000[100 – 0,25(100 – Q)]
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23. Financial Innovations and Product Design II
Interest Rate Markets
Duration:
A measure of how long on average the holder of a bond has to wait before receiving cash payments.
The duration can be used to estimate bond price changes as a result of yield changes:
B – bond price
y – yield
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24. Financial Innovations and Product Design II
Interest Rate Markets
Duration:
When y is expressed with compounding m times per year, the Modified duration should be used:
Duration of a portfolio: weighted average of the durations of the individual bonds in the portfolio, with the weights being proportional to the bond prices
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25. Financial Innovations and Product Design II
Interest Rate Markets
Duration:
Hedging using duration:
Hedging against interest rate risk by matching the durations of assets and liabilities
Financial Innovations and Product Design II

26. Financial Innovations and Product Design II
Interest Rate Markets
Duration:
Problems:
Hedging works only when there are parallel shifts in the yield curve
Unaccurate for larger yield changes
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27. Financial Innovations and Product Design II
Interest Rate Markets
Convexity:
Eliminates some of the unaccuracy caused by the duration when estimating price changes resulting from larger yield changes
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28. Financial Innovations and Product Design II
Swaps
Swap:
An agreement between two companies to exchange cash flows at specified future times according to specified rules
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29. Financial Innovations and Product Design II
Swaps
Interest rate swap:
One company agrees to pay cash flows equal to interest at a predetermined fixed rate on a notional principal and in return receives interest at a floating rate on the same notional principal
The notional principal itself is not exchanged
„Plain vanilla“ swap
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30. Financial Innovations and Product Design II
Swaps
Interest rate swap:
Assets and liabilities can be converted from fixed rate to floating rate & vice versa
Trasforming a liability (example):
Microsoft borrows at LIBOR + 10 bps
Intel borrows at 5,2% fixed
Microsoft & Intel enter into a swap:
Microsoft pays 5% and receives LIBOR
Intel pays LIBOR and receives 5%
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31. Financial Innovations and Product Design II
Swaps
Interest rate swap:
Trasforming a liability:
Result:
Intel pays LIBOR + 20bps
Microsoft pays 5,1% fixed 5%
5.2%
Intel MS
LIBOR+0.1%
LIBOR
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32. Financial Innovations and Product Design II
Swaps
Interest rate swap:
Financial intermediary:
Usually two nonfinancial companies do not get in touch directly to arrange a swap – deal each deal with a financial intermediary (FI)
The FI enters into two offsetting swap transactions with the two companies and earns about 3-4bps
Because the FI has two separate contracts, it bears the default risk of one of the companies in the swap and still has to honor the remaining contract
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33. Financial Innovations and Product Design II
Swaps
Interest rate swap:
Financial intermediary:
Large FIs act as market makers, i.e. they are prepared to enter into a swap without an offsetting swap with another counterparty
Result:
Microsoft pays 5,115%
Intel pays LIBOR + 21,5bps
The FI earns 3bps
4.985%
5.015%
5.2%
Intel
F.I. MS
LIBOR+0.1%
LIBOR
LIBOR
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34. Financial Innovations and Product Design II
Swaps
Interest rate swap:
Why are swaps so popular?
Comparative advantage argument: some companies have a comparative advantage in floating rate markets whereas others have a comparative advantage in fixed rate markets
Fixed
Floating
AAACorp
10.00%
6-month LIBOR %
BBBCorp
11.20%
6-month LIBOR %
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35. Financial Innovations and Product Design II
Swaps
Interest rate swap:
Why are swaps so popular?
Result:
AAA now pays LIBOR + 5bps (compared to LIBOR + 30bps)
BBB now pays 10,95% fixed (compared to 11,2%)
9.95%
10%
AAA
BBB
LIBOR+1%
LIBOR
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36. Financial Innovations and Product Design II
Swaps
Interest rate swap:
Criticism of the comparative advantage argument:
The fixed rate remains the same throughout the life of the swap whereas the floating rate is reset at constant intervals
This creates a problem to the company that transforms its floating rate obligation into a fixed rate
The amount fixed rate interest paid depends on the way the original floating rate is reset, i.e. if BBB was downgraded to a lower credit rating this would be reflected in a higher floating rate and thus increasing the amount of interest BBB has to pay
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37. Financial Innovations and Product Design II
Swaps
Interest rate swap:
Valuation using bonds:
The value of a swap can be characterized as the difference between two bonds – one paying a fixed coupon and one paying a floating rate coupon
The value of a swap to a company receiving floating and paying fixed is then:
Vswap = Bfl - Bfix
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38. Financial Innovations and Product Design II
Swaps
Interest rate swap:
Valuation using bonds:
Value of a floating-rate bond?
Immediately after payment date, Bfl = principal
Between payments:
k*: floating-rate payment that will be made on the next payment date
L: notional principal
t1: time until the next payment date
-r1t1
Bfl = (L+k*)e
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39. Financial Innovations and Product Design II
Swaps
Interest rate swap:
Swap rates: the average of Bid and Offer rates quoted by market makers in the swap market
Bid rate: the fixed rate in a contract where the market maker will pay fixed and receive floating
Offer rate: the fixed rate in a contract where the market maker will pay floating and receive fixed
Swap rates can be used to determine zero rates:
Consider a new swap where the fixed rate equals the swap rate, then we have:
Bfl = Bfix
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40. Financial Innovations and Product Design II
Swaps
Interest rate swap:
Swap rates can be used to determine zero rates:
The floating-rate bond will be worth par
Thus, the fixed-rate bond will be worth par as well – the swap rate is the par yield of the fixed-rate bond
As a result, zero rates can be extracted using the bootstrap method
Swap rates are used to calculate the zero curve for longer maturities
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41. Financial Innovations and Product Design II
Swaps
Currency swap:
In its simplest form it involves exchanging principal and interest payments in one currency for principal and interest payments in another currency
The principal amounts are usually exchanged at the beginning and at the end of the swap‘s life
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42. Financial Innovations and Product Design II
Swaps
Currency swap:
Example:
Swap between IBM and BP
IBM pays a fixed rate of interest 11% in Pounds and receives a fixed rate of interest of 8% in dollars
IBM‘s cash flows
Dollars
Pounds $
Year
------millions------
2001
–15.00
+10.00
2002
+1.20
–1.10
2003
+1.20
–1.10
2004
+1.20
–1.10
2005
+1.20
–1.10
2006
+16.20
-11.10
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43. Financial Innovations and Product Design II
Swaps
Currency swaps:
Valuation:
Using bonds: if S0 is the exchange rate (number of domestic currency per unit of foreign currency), BD the value of the domestic bond, BF the value of the foreign bond (in foreign currency units), the value to the party receiving domestic currency and paying foreign currency is:
Using forwards: the swap is decomposed into a series of forward contracts
Vswap = BD – S0BF
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44. Financial Innovations and Product Design II
Swaps
Credit risk:
A swap is worth zero to a company initially
At a future time its value is liable to be either positive or negative
The company has credit risk exposure only when its value is positive
While market risks can be hedged by entering into offsetting contracts, credit risks are less easy to hedge
Financial Innovations and Product Design II

45. Thank You for Your Attention!
Financial Innovations and Product Design II