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…
Backward Induction
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…
Binomial Interest Rate Model
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….
The Gordon Growth Model
The Gordon growth model assumes that dividends grow indefinitely at a constant rate. $$D_t= D_{t-1} (1+g)$$ Where: \(g =\) Expected constant growth rate in dividends \(D_{t}=\) Expected dividend at time t. At any time \(t\), \(D_{t}=\) equals dividends at \(t =…
The Dividend Discount Model
Single Holding Period The cash flows to an investor who holds shares are the dividends paid and the market price of the share when they sell the share. For example, suppose an investor expects to hold the share for one…
Arbitrage Free Value
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…
