Effective Durations of Callable, Putable, and Straight Bonds
Callable Bonds The effective duration of a callable bond cannot be greater than that of a straight bond. As interest rates rise above the coupon rate, the call option becomes out of money. Therefore, straight and callable bonds will have…
Effective Duration of Bonds with Embedded Options
Effective duration is the sensitivity of a bond’s price to a 1% parallel shift in the benchmark yield curve, assuming that the credit spread of the bond remains constant. Effective (option-adjusted) duration is the most appropriate measure for bonds with…
Interest Rate Volatility and Option-Adjusted Spreads (OAS)
The option-adjusted spread (OAS) depends on the interest rate volatility assumption. For a callable bond, the OAS decreases as the interest rate volatility increases, and vice versa. A high volatility assumption generates a higher value for a call option, while…
Option-adjusted Spreads
A workable approach employed in constructing a suitable yield curve for risky bonds involves adding a fixed Z-spread to the one-year forward rates derived from the default-free spot yield curve. Recall that Z-spread is the basis point spread that would…
Valuing Bonds with Embedded Options
The steps for valuing a bond with an embedded option in the presence of interest rate volatility are as follows: Step 1: Generate an interest rate tree using the yield curve and interest rate volatility assumptions. Step 2: Determine whether…
How the Shape of the Yield Curve Affects the Value of Embedder Bonds
The value of a callable or putable bond is also affected by changes in the level and shape of the yield curve. Callable bond The Level Effect As interest rates decrease, the value of a straight bond increases. However, part…
Interest Rate Volatility
The value of embedded options increases as interest rate volatility increases. This is because embedded options have a higher chance of being exercised when the volatility is high. Callable Bond As the interest rate volatility increases, the value of a…
Using Arbitrage Free Framework to Value Bonds with Embedded Options
Recall that given either spot rates, forward rates, or par rates, one can determine the value of a straight bond by discounting its cashflows. However, valuing the embedded option requires one-period forward rates. This is because we work out the…
Valuing Embedded Options
According to the arbitrage-free framework, the value of a bond with embedded options is the sum of the arbitrage-free value of the option-free bond (straight bond) and the arbitrage-free values of any embedded options. Embedded Calls A callable bond is…
Fixed Income Securities with Embedded Options
Embedded options give either the issuer of a bond or the bondholder the right to take advantage of movements in interest rates. Embedded options are attached to a straight (option-free) bond. This makes them bond-dependent, and hence they cannot be…
