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7.2 Overview of Arbitrage Valuation of a Fixed-Income Instrument

Arbitrage-free valuation refers to an approach to security valuation that determines security values that are consistent with the absence of arbitrage opportunities.

The traditional approach to valuing bonds is to discount all cash flows with the same discount rate as if the yield curve were flat.

However, the yield curve is rarely flat. Thus, each cash flow of the bond should be discounted at the appropriate spot rate. This leads to arbitrage-free value.

  • Think of the valuation of a bond as a portfolio of zeros.

Regardless of the complexity of the bond, each component (coupons, par values) must have an arbitrage-free value. A bond with embedded options can be valued in parts as the sum of the arbitrage- free bond without options (that is, a bond with no embedded options) and the arbitrage-free value of each of the options.

ARBITRAGE OPPORTUNITIES Arbitrage opportunities arise as a result of violations of the law of one price. There are two types of arbitrage opportunities.

  • Value additivity, which means the value of the whole equals the sum of the values of the parts
  • Dominance, where a financial asset with a risk-free payoff in the future must have a positive price today The law of one price states that two goods that are perfect substitutes must sell for the same current price in the absence of transaction costs. Otherwise, if it were costless to trade, one would simultaneously buy at the lower price and sell at the higher price.

IMPLICATIONS OF ARBITRAGE-FREE VALUATION

  • Using the arbitrage-free approach, any fixed-income security should be thought of as a package or portfolio of zero-coupon bonds.
  • Stripping – Dealers in US Treasuries can separate the bond's individual cash flows and trade them as zero-coupon securities. This process is called "stripping."
  • Reconstitution – Dealers can recombine the appropriate individual zero-coupon securities and reproduce the underlying coupon Treasury. This process is called "reconstitution."
  • The arbitrage-free valuation approach does not allow a market participant to realize an arbitrage profit through stripping and reconstitution.

Lesson Wrap-Up

This lesson should leave you able to explain the overview of arbitrage valuation of a fixed-income instrument in a fixed-income context and connect it to the decisions made by issuers, investors, or analysts.

Review Prompts

  1. Explain overview of arbitrage valuation of a fixed-income instrument in your own words.
  2. State one exam-style risk, valuation, or market implication of the overview of arbitrage valuation of a fixed-income instrument.