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.
Key Rate Generalization #1
-If option-free bond is trading at par, the bond’s maturity-matched rate is the only rate that affects the bond’s value.
Key Rate Generalization #2
-For an option-free bond not trading at par, the maturity-matched rate is still the most important rate.
Key Rate Generalization #3
-A bond with low (or zero) coupon rate may have negative key rate durations for horizons other than bond’s maturity
Key Rate Generalization #4
- A callable bond with a low coupon rate is unlikely to be called; hence, the bond’s maturity-matched rate is most critical.
- Higher coupon bonds are likely to be called, and therefore the time-to-exercise rate will tend to dominate the time-to-maturity rate.
Key Rate Generalization #5
- A putable bond with a high coupon rate is unlikely to be put; hence, the bond’s maturity-matched rate is most critical.
- Lower coupon bonds are likely to be put, and therefore the time-to-exercise rate will tend to dominate the time-to-maturity rate.
Callable, Putable and Straight convexity
- Straight bonds have positive convexity: the increase in value of an option-free bond is higher when rates fall than the decrease in value when rates increase by an equal amount.
- When rates are high, callable bonds are unlikely to be called and will exhibit positive convexity. When underlying call option is near the money, its effective convexity turns negative; the upside potential of the bond’s price is limited due to the call.
-PUTABLE bonds exhibit positive convexity throughout
Floating Rate Bond
- Pays a coupon that adjusts every period based on an underlying reference rate .
- Typically paid in arrears: coupon rate is determined at the beginning of a period but is paid at the end of period.
Capped floater
-contains an issuer option that prevents the coupon rate from rising above a certain level.
Value of capped floater = value of straight floater - value of embedded cap
Floored floater
-coupon rate will not fall below a certain level
value of floored floater = value of straight floater + value of embedded floor
Convertible bond
-has the right to convert the bond into a fixed number of common shares of the issuer during a specified timeframe (conversion period) and at a fixed amount of money (conversion price)
***lower yield, but upside on issuer stock. Issuer benefits from lower borrowing cost, but existing shareholders may face dilution on conversion.
Conversion ratio
-number of common shares for which a convertible bond can be exchanged.
@ issue price not current
Contingent Put options
- merger
- higher dividend
- change of control
Conversion value
Market price of stock x conversion ratio
Min value of convertible bond
Max (straight value, conversion value)
Market conversion price
Market price of convertible bond/conversion ratio
-stock price at which investor is undecided t between selling and converting a bond
Market conversion premium ratio
Market conversion premium per share/market price did common stock
Market conversion premium = market conversion price - stock market price
Premium over straight value
(Market price of convertible bond/straight value) - 1
-the greater the premium over straight value, the less attractive the bond.
Value of convertible bond
Convertible, non callable bond = straight value + value of call option on stock
