R.34 Term Structure and Interest Rate Dynamics Flashcards
Spot and forwards rates
- Price for each
- Forward rate model
- Relationship
Key Rate Durations
(no need to calculate. Know relationships!)
Duration assumes parallel interest rate shift (short, interm, long all move the same). Problem is that usually rate shifts have curvature. So….
Rate duration is what happens to change in value of bond if we change just one spot-rate (par rates)
Key rate duration takes multiple rate durations to analyze impact on bond value.
- Option-FREE bond = maturity match rate most important. key rate highest b/c biggest CF at maturity.
Measures bond price sensitivity to a change in a specific par rate, keeping everything else constant.
Modern Term Structure Models:
- Equilibrium term structure models
- Arbitrage-free models
1. Equilibrium term structure models
-
Cox-Ingersoll-Ross (CIR) model:
- __dr = a(b−r)dt + σ √(rdz)
- Assumes the economy has a natural long-run interest rate (b) that the short- term rate (r) converges to.
-
Vasicek model:
- dr = a(b – r)dt + σdz
- Similar to the CIR model but assumes that interest rate volatility level is independent of the level of short-term interest rates.
2. Arbitrage-free models—Begins with observed market prices and the assumption that securities are correctly priced.
- Ho-Lee model: drt = θtdt + σdzt
- This model is calibrated by using market prices to find the time-dependant drift term θt that generates the current term structure.
Factors driving Yield Curve?
- Effective duration—Measures the sensitivity of a bond’s price to parallel shifts in the benchmark yield curve.
- Key rate duration—Measures bond price sensitivity to a change in a specific par rate, keeping everything else constant.
- Sensitivity to parallel, steepness, and curvature movements—Measures sensitivity to three distinct categories of changes in the shape of benchmark yield curve
Spread formulas and definitions
- Swap spread
- TED spread
- LIBOR-OIS Spread
- Z-spread
Swap spreadt = swap ratet - Treasury yieldt
- additional interest rate paid by fixed-rate payer of interest rate swap over the rate of the “on-the-run” government bond of same maturity.
TED spread = (3-month LIBOR) - (3-month T-Bill)
- Difference between rates on interbank loans and short-term U.S. govt debt (“T-bills”). TED is T-Bill and ED, the ticker symbol for the Eurodollar futures contract.
- Indicates overall level of credit risk in the economy.
LIBOR-OIS spread = LIBOR rate - “overnight indexed swap” rate
- is the amount by which the LIBOR rate (which includes credit risk) exceeds the overnight indexed swap (OIS) rate (which includes only minimal credit risk). The LIBOR-OIS spread is a useful measure of credit risk and provides an indication of the overall well-being of the banking system.
Z-spread = spot ratet - (PV of CFs = bond’s mkt price)
- Zero-volatility spread (assume rate volatility zero)
- Not appropriate for embedded options (use Z for straight only)
- –when added to each spot rate on the yield curve, makes the present value of a bond’s cash flows equal to the bond’s market price.
OAS
- option adjusted spread
- if straight, then OAS and Z-spread are equal
Credit spread => ☺make fun of.
- simple and likely not used in level 2.
- = YTM credit-risky ZeroCpn - YTM risk-free ZeroCpn
Traditional Theories (5) of the
Term Structure of Interest Rates
- Unbiased expectations theory—Forward rates are an unbiased predictor of future spot rates. Also known as the pure expectations theory.
- Local expectations theory—Preserves the risk-neutrality assumption only for short holding periods, while over longer periods, risk premiums should exist. This implies that over short time periods, every bond (even long-maturity risky bonds) should earn the risk-free rate.
- Liquidity preference theory—Investors demand a liquidity premium that is positively related to a bond’s maturity.
- Segmented markets theory—The shape of the yield curve is the result of the interactions of supply and demand for funds in different market (i.e., maturity) segments.
- Preferred habitat theory—Similar to the segmented markets theory, but recognizes that market participants will deviate from their preferred maturity habitat if compensated adequately.
Level and Shape of Yield Curve
- Impact of rates up/down on calls and puts?
- Yield curve steepens?
- Yield curve flattens?
- Upside on callable limited when rates decline
- Downside on putable limited when rates increase
- Steepened curve makes call option unlikely to be exercised and has low value while put option is valuable
- Flattened curve makes call option become more valuable while put option losses value.
One-Sided Durations
Callable bonds → lower one-sided down-duration (rates ↓ not price!) than one-sided up-duation
Putable bonds → HIGHER one-sided down-duration than one-sided up-duration