Fixed Income Derivatives: Forwards, Futures, and Swaps
Introduction to Fixed Income Derivatives
1. Introduction
A derivative is a security whose value depends on the value of another security. Hedgers include oil producers, farmers, and other commodity producers.
2. Over-the-Counter Markets (OTC)
A decentralized market where dealers are connected through telephone, the internet, and proprietary electronic trading systems (for forwards and swaps).
- Advantages: Terms of contracts are privately negotiated.
- Disadvantages: Counterparty risk.
3. Exchange-Traded Markets
A centralized market where securities, commodities, and derivatives are traded, with a clearinghouse in the middle.
4. Forwards
- Forward contract: An agreement between two counterparties to purchase and sell a security at a specific price and time in the future.
- Forward rate: The interest rate today for a future loan.
- Spot rates are interest rates today.
- Forward rate agreement (FRA): Used to lock in future interest rates and protect against increases.
5. Futures
A future contract is an agreement for the delivery of an asset at a future date, at an agreed-upon future price (traded on an exchange).
6. Mechanics of Trading
- Clearinghouse: Acts as an intermediary for all trades.
- Market position:
- Long to buy future contracts.
- Short to sell future contracts.
- Liquidating position: Liquidate prior to or on contract maturity.
- Most liquidate before contract maturity.
- Offset (reverse) trade (have a long position and take a short position).
7. Margin
- The amount of money that must be deposited in a margin account to open a future position (about 5-15% of the contract value).
- The clearinghouse has margin requirements.
- Two types: initial and maintenance margins.
- Account value: Mark-to-market.
8. Margin Call
When the maintenance margin is reached, the broker will ask for additional margin funds.
9. Convergence Property
The future price and spot price must converge at the maturity of the contract.
10. Profits
- Profit to long position: Future Price (T) – Price (0) = Spot Price (T) – Price (0)
- Profit to short position: Price (0) – Future Price (T) = Price (0) – Spot Price (T)
11. Pricing of Future Contracts
Future Price = Spot Market Price * (1 + t(r – current yield or coupon rate divided by the spot market price))
- Cost to carry = r – c
- c > r: Positive carry (future contract sells at a discount)
- c < r: Negative carry (future contract sells at a premium)
12. Interest Rate Swaps
An interest rate swap (IRS) is an agreement between two parties to exchange payments of two bonds.
The most popular IRS is a fixed-for-floating swap.
- One party makes payments based on a fixed rate and receives payments based on floating interest rates.
- Both have the same principal, maturity, and payment dates.
- Example: A firm issues fixed-rate debt and expects rates to fall.
- It enters a swap transaction (receives fixed payments, pays floating rates).
13. Credit Default Swaps (CDS)
A negotiated bilateral contract for protection against the risk of default on debt obligations.
- The buyer must pay a premium.
- Credit events cause the CDS to be triggered.
- Physical settlement: The protection buyer delivers the debt obligation to the seller in exchange for par value.
- Cash settlement: The protection seller pays an amount equal to par less the market value of the reference bond.
- Risk profile of CDS:
- Modeling is difficult (illiquid, true default probabilities are hard to judge, asymmetric information).