Interest Rate Swap
In an interest rate swap, two parties agree to exchange periodic interest payments. The amount of the interest payments exchanged is based on some
Payer and receiver are always from the fixed rate angle. Receiver receives kind of a long term bond (although won’t get the principal) ⇒ face higher interest rate (with bigger duration)
The floating rate is “reset” on the reset date (beginning date of each period). Payments are also payed on reset dates.
Computing the fixed swap rate
The requirement is that the hedged swap have zero net present value
thus
note that are viewed as “discount”, it means, the sum of the forward rates discounted by spot rates should be the same with the sum of swap rate discounted by spot rates.
An alternative way to express the swap rate is
It can be proved that (intuitively), the swap rate is the coupon rate on a par coupon bond.
An example is shown as following
Above values are the values in title, if the swap is closed, the payer whose value is only (should be) 99.805 now should compensate the receiver, whose value is (should be) 102.685.
During the financial crisis, the swap spread increase dramatically and became more fluctuated.
The hedge part include Short Bond in Bond market, and Earn reverse repo in repo market.
LIBOR is higher than repo rate because there is collateral for repo but none for LIBOR.
Applications of interest rate swap
Portfolio management: adjust interest rate exposure and offset the risks posed by interest rate volatility
Speculation: Swap require little capital up front
Corporate finance: Match asset maturity or income stream
Risk management: Hedge with interest rate swaps
Rate-locks on bond issuance: Lock in the current interest rate by entering into swap contracts paying fixed rates.
Forward and Futures
Forward Contract
Futures Contract
Futures are financial derivatives that obligate the contract holder to purchase or sell an underlying aseet (or its cash value) on a specified date at a predetermined price.
- A futures contract trades on a future exchange market and is bought or sold through a brokerage firm that offers futures trading
- The terms (price and the expiration date) are decided at the time the future is purchased or sold
- Futures contract is used for hedging, speculating, or arbitrage
Margin and Marking-to-market
Key features:
- Standardized
- Created by exchange and cleared by clearing house
- Highly liquid
- Marking to market
- Margin required
Financial futures: stock index futures, interest rate futures, and currency futures.
Treasury Futures
Conversion factor
Futures price is quoted on a reference bond with maturity of, say 5 years and yield of, say 3%. Upon maturity, the seller must deliver some eligible bonds, which meet the maturity specifications of a Treasury futures contract, in exchange for an invoice price. Conversion factors link the different prices of the eligible bonds and the price of the reference bond.
Conversion factor for CFFEX
Conversion does not change over time, and only depends on
Review: How to compute the clean price ?
Delivery options (choices)
- Quality option: the seller can deliver any eligible bonds — cheapest to deliver (CTD), good choice for the seller.
- Timing option: the delivery notice can be given in a period (the expiration month), not only on a date
- Wildcard option: The futures exchange closes early (4:00 pm Chicago time) in the afternoon, but bonds keep trading. The seller can announce delivery any time until the bond markets close (8:00 pm Chicago time). Leave more time for the seller.
- End-of-month option (close-out): The futures stop trading before the end of the month (8 business days for the long-term US bond futures)
Implied repo rate
where is the future price determined at time ; CF is the conversion factor. Besides, we should consider the interim coupon if paid between and .
Basis after carry (BAC) or net basis
where
(interest income, purchase cost)
Thus,
the bond having the lowest BAC, it’s the cheapest-to-deliver (and most likely to be the cheapest-to-deliver in the near future)
Interest Rate Option
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