R.35 Arbitrage-Free Valuation Framework Flashcards
LEARNING OUTCOMES The candidate should be able to: explain what is meant by arbitrage-free valuation of a fixed-income instrument; calculate the arbitrage-free value of an option-free, fixed-rate coupon bond; describe a binomial interest rate tree framework; describe the backward induction valuation methodology and calculate the value of a fixed-income instrument given its cash flow at each node; describe the process of calibrating a binomial interest rate tree to match a specific term stru
R. 35 Path wise valuation
Pathwise valuation can be used instead of backward induction to value cash flows. Pathwise valuation calculates the present value for each possible interest rate path. There are three steps for pathwise valuation. 1. Specify all paths through the tree. 2. Determine the present value of the bond along each path. 3. Calculate the average present value from all the paths. The number of paths and associated probabilities can be determined from Pascal’s triangle. For example, after three time periods there are four potential ending nodes and eight paths to get there.
Binomal Interest Rate Tree Framework Bond value at any node Backward induction
In a binomial interest rate tree framework, there are two possible interest rates in the next period that will be consistent with: 1. An interest rate model that governs the random process of interest rates 2. The assumed interest rate volatility 3. The current benchmark yield curve Backward induction method: Works from right to left, starting at maturity where the value of bond is known. Assumes 50% probability going upp (VH) or down (VL).
