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…

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…

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…

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 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…

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…

Backward induction involves working backward from maturity to time 0 to determine a bond’s value at each node. It makes the following assumptions: The value of a bond is known at maturity (Final coupon payment + Face value). The value…

Modeled future interest rates can take on different possible values, depending on the level of volatility assumed. This can be shown using an interest rate tree framework. One of the most popular tools used is the binomial interest rate model….

Bonds can be valued either using the traditional valuation approach or the arbitrage-free valuation approach. Under the traditional valuation approach, a single interest rate is used to discount all of a bond’s cash flows. In this approach, all cash flows of…

Arbitrage free valuation is an approach that determines bond values based on the assumption that arbitrage opportunities do not exist. The arbitrage-free valuation model is based on the law of one price, which states that two goods, which are perfect…