Capped and floored floaters can be valued using the arbitrage-free framework. Valuation of a Capped Floater A capped floater (floating rate loan) is a bond that pays a coupon that resets every period based on the reference rate. Reference rates…

Effective convexity is the sensitivity of duration to changes in interest rates. $$ \text{Effective convexity} =\cfrac {P_{i-}+P_{i+}-2 \times P_o}{P_0 (\Delta \text{Curve})^2} $$ Both callable and straight bonds experience similar positive convexity when interest rates are high. However, the effective convexity…

One-sided Duration Bonds with embedded options have asymmetrical price sensitivity to up or down interest rate movements of the same magnitude. When the embedded option is in the money, the price of a callable bond has limited upside potential, while…

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 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…

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…

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…

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…

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…

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…