Reading 30: Valuation and Analysis of Bonds with Embedded Options Flashcards
Embedded option
1) help manage interest rate risk
2) issue bonds at an attractive coupon rate
Callable Bonds
- give the issuer the option to call back the bond, the investor is short the call option
- typically have call protection period during which the bonds cannot be called
- can be American, European or Bermudan
Vcall = Vstraight - Vcallable
Putable Bonds
- allow investor to put (sell) bond back to issuer prior to maturity
- investor is long underlying put option
- ***extendible bond is related
V putable = Vstraight + Vput
Vput = Vputable - Vstraight
Estate Put
- includes provision that allows heirs of an investor to put the bond back to the issue upon death of the investor.
- Value of bond is inversely related to investor life expectancy
Sinking funds bonds
- require the issuer to set aside funds periodically to retire the bond (sinking fund)
- reduces credit risk of bond
Binomial tree options
- instead of using spot rates, one-period forward rate are used.
- Call Rule: Any node where the bond is callable must be either the price at which the issuer will call the bond or the computed value if the bond is not called, whichever is lower.
- Put Rule: Any node where the bond is putable must be either the price at which the issuer will put the bond or the computed value if the bond is not called, whichever is higher.
Level of interest rates
- As interest rates decline, the short call in a callable bond limits the bonds upside, so the value of a callable bond rises less rapidly than the value of an otherwise-equivalent straight bond
- As interest rates increase, the long put hedges against the loss in value; the value of a putable bond falls less rapidly than the value of an otherwise-equivalent straight bond
Shape of yield curve
- Value of embedded call option increases as interest rates decline
- therefore value of call option will be lower for upward sloping yield curve
Option adjusted spread (OAS)
- backward induction uses risk free rates which will calculate too high value, must use risk.
- Must add OAS to all one-period rates in the tree such that the calculated value equals the market price of the risky bond.
- bonds with low OAS relative to peers are considered to be overvalued
- OAS calculated depends on volatility assumed
- **added to tree after adjustment for embedded option
Relationship between volatility and OAS
Value
Vol Level | Calls Puts Callable Putable | OAScall OASput
High High High Low High Low High
Low Low Low High Low High Low
Effective Duraiton
[(estimated price if yield decreases by x) - (estimated price if yield decreases by x)]/
(2 x original price * change in required yield)
Effective Convexity
[(estimated price if yield decreases by x) + (estimated price if yield decreases by x) - (2* original price)] / (original price * change in required yield^2)
Life of bond with options
-effective duration (callable)
One-sided durations
-For bonds with embedded options, one sided duration - durations that apply only when interest rates rise of fall are better at capturing IR sensitivity than effective duration.
- For a callable bond, when the call option is at or near the money, the change in price for a decrease in yield will be less than the change in price for an equal amount of increase in yield. The value of a callable bond is capped by its call price.
- Callable bonds will have lower on-sided down duration than one sided up-duration (AKA: the price change of a callable when rates fall is smaller than the price changed for an equal increase in rates).
Key Rate Duration
- Captures interest rate sensitivity of a bond to changes in yield (par rates) of specific benchmark maturities.
- Used to identify the interest rate risk from changes in shape. SHAPING RISK.
