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…
Monte Carlo Forward Rate Simulation
The Monte Carlo simulation is an alternative method of modeling interest rates that works by generating a large number of potential interest rate paths to discover how the value of a security may be impacted over time. The paths are…
Pathwise Valuation
Pathwise valuation involves discounting a bond’s cash flows for each likely interest rate path and calculating the average of these values across all the paths. It is an alternative method to the backward induction approach. The following steps are involved…
Calibrating a Binomial Interest Rate Tree
The following steps should be followed when calibrating binomial interest rate trees to match a particular term structure: Step 1: Estimate the appropriate spot and forward rates for a known par value curve. Step 2: Construct the interest rate tree…
