34. Valuation and Analysis of Bonds with Embedded Options

Question 1

Embedded Options

Answer 1

Contingency provisions found in a bond’s indenture or offering circular representing rights that enable their holders to take advantage of interest rate movements. They can be exercised by the issuer, by the bondholder, or automatically depending on the course of interest rates.

Question 2

Straight Bond

Answer 2

An underlying option-free bond with a specified issuer, issue date, maturity date, principal amount and repayment structure, coupon rate and payment structure, and currency denomination.

Question 3

Callable Bond

Answer 3

Bond that includes an embedded call option that gives the issuer the right to redeem the bond issue prior to maturity, typically when interest rates have fallen or when the issuer’s credit quality has improved.

Question 4

Putable Bond

Answer 4

Bond that includes an embedded put option, which gives the bondholder the right to put back the bonds to the issuer prior to maturity, typically when interest rates have risen and higher-yielding bonds are available.

Question 5

Lockout Period

Answer 5

Period during which a bond’s issuer cannot call the bond.

Question 6

Extendible Bond

Answer 6

Bond with an embedded option that gives the bondholder the right to keep the bond for a number of years after maturity, possibly with a different coupon.

Question 7

Sinking Fund Bond

Answer 7

A bond which requires the issuer to set aside funds over time to retire the bond issue, thus reducing credit risk.

Question 8

Value of Bond with Embedded Options

Answer 8

The value of a bond with embedded options is equal to the sum of the arbitrage-free value of the straight bond and the arbitrage-free values of the embedded options.

Question 9

The procedure to value a bond with an embedded option in the presence of interest rate volatility:

Answer 9

Generate a tree of interest rates based on the given yield curve and interest rate volatility assumptions.

At each node of the tree, determine whether the embedded options will be exercised.

Apply the backward induction valuation methodology to calculate the bond’s present value. This methodology involves starting at maturity and working back from right to left to find the bond’s present value.

Question 10

Option Adjusted Spread

Answer 10

(OAS) Constant spread that, when added to all the one-period forward rates on the interest rate tree, makes the arbitrage-free value of the bond equal to its market price.

Question 11

Effective Duration

Answer 11

Sensitivity of the bond’s price to a 100 bps parallel shift of the benchmark yield curve, assuming no change in the bond’s credit spread.

Question 12

Key-Rate Duration

Answer 12

Sensitivity of a bond’s price to changes in specific maturities on the benchmark yield curve. Also called partial durations.

Question 13

One-Sided Duration

Answer 13

Effective durations when interest rates go up or down, which are better at capturing the interest rate sensitivity of bonds with embedded options that do not react symmetrically to positive and negative changes in interest rates of the same magnitude.

Question 14

Effective Convexity

Answer 14

Sensitivity of duration to changes in interest rates.

Question 15

Capped Floater

Answer 15

Floating-rate bond with a cap provision that prevents the coupon rate from increasing above a specified maximum rate. It protects the issuer against rising interest rates.

Question 16

Floored Floater

Answer 16

Floating-rate bond with a floor provision that prevents the coupon rate from decreasing below a specified minimum rate. It protects the investor against declining interest rates.

Question 17

Convertible Bond

Answer 17

Bond with an embedded conversion option that gives the bondholder the right to convert their bonds into the issuer’s common stock during a pre-determined period at a pre-determined price.

Question 18

Conversion Period

Answer 18

For a convertible bond, the period during which bondholders have the right to convert their bonds into shares.

Question 19

Conversion Price

Answer 19

For a convertible bond, the price per share at which the bond can be converted into shares.

Question 20

Conversion Ratio

Answer 20

For a convertible bond, the number of shares of common stock that a bondholder receives from converting the bond into shares.

Question 21

Forced Conversion

Answer 21

For a convertible bond, when the issuer calls the bond and forces bondholders to convert their bonds into shares, which typically happens when the underlying share price increases above the conversion price.

Question 22

Conversion Value

Answer 22

For a convertible bond, the value of the bond if it is converted at the market price of the shares. Also called parity value.

Question 23

Minimum Value of a Convertible Bond

Answer 23

The minimum value of a convertible bond is equal to the greater of

the conversion value and

the value of the underlying option-free bond. Theoretically, the value of the straight bond (straight value) can be estimated by using the market value of a non-convertible bond of the issuer with the same characteristics as the convertible bond but without the conversion option. In practice, such a bond rarely exists. Thus, the straight value is found by using the arbitrage-free framework and by discounting the bond’s future cash flows at the appropriate rates.

Question 24

Market Conversion Premium Per Share

Answer 24

For a convertible bond, the difference between the market conversion price and the underlying share price, which allows investors to identify the premium or discount payable when buying a convertible bond rather than the underlying common stock.

Question 25

Market Conversion Premium Ratio

Answer 25

For a convertible bond, the market conversion premium per share expressed as a percentage of the current market price of the shares.