• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar
  • Skip to footer
Finance Train

Finance Train

High Quality tutorials for finance, risk, data science

  • Home
  • Data Science
  • CFA® Exam
  • PRM Exam
  • Tutorials
  • Careers
  • Products
  • Login

Valuing an Option Embedded Bond using Binomial Interest Rate Tree

CFA® Exam, CFA® Exam Level 2, Fixed Income Securities

This lesson is part 16 of 17 in the course Fixed Income Part 1

The Binomial Interest Rate Tree

An issuer’s bonds can be valued with a binomial interest rate tree. In order to do this, the analyst will need to:

  • Calculate the spot rate curve for the borrower based on that company’s most recently issued debt.
  • Use the spot rate curve to calculate forward rates for the issuer.
    • Applying forward rates when discounting cash flows is arbitrage free valuation.
  • Develop a higher and lower interest rate scenario around each projected forward rate on the tree, based on an estimation of interest rate volatility.
  • If necessary, adjust the tree so it properly values the currently issued bonds.
    • If the tree leads to a bond value that is above the market price, then interest rates will need to be increased; if the tree leads to a bond value that is below the market price, then interest rates will need to be lowered.
  • For bonds with embedded options, cash flows will need to be forecasted along all of the interest rate paths; these cash flows will need to be discounted to the present value to create a value for the bond.

Valuing an Option Embedded Bonds

Valuing a Callable Bond from a Binomial Interest Rate Tree

  • When valuing a callable bond with a binomial interest rate tree, the analyst must assume that the bond will be called back by the issuer when the strike price is exceeded.
  • At any nodes where the calculated bond price exceeds the call price, the calculated price is replaced with the call price.

Valuing a Putable Bond from an Binomial Interest Rate Tree

  • When valuing a putable bond with a binomial interest rate tree, the analyst must assume that the bond will be put back to the issuer when the price falls below the put floor.
  • At any nodes where the calculated bond price is below the put price, the calculated price is replaced with the put price.

The Value of an Embedded Option

Price callable bond = Price ncb – Call option value

 

The price of a callable bond is lower than that of a comparable bond that does not contain an embedded option.

Price putable bond = Price npb + Put option value

 

The price of a putable bond is higher than that of a comparable bond that does not contain an embedded option.

  • Put options increase the cost of the bond to the investor as they serve as an “insurance policy” that the value of the bond cannot drop below the floor established by the put.
  • Call options reduce the cost of the bond to the investor as the call serves creates a ceiling for the borrower. By embedding a call option in its bond issuance, the borrower is preserving the ability to refinance its debt on more favorable terms, should interest rates drop significantly.
  • The Effect of Interest Rate Volatility on the Value of Embedded Options
    • As interest rate volatility increases, so do the value of embedded options.
    • For example, in the case of a putable bond, the value of the embedded put goes up when interest rate volatility increases. This increases the purchase price of the putable bond to the investor.
Previous Lesson

‹ Benchmark Yield Spreads

Next Lesson

How to Price Convertible Bonds? ›

Join Our Facebook Group - Finance, Risk and Data Science

Posts You May Like

How to Improve your Financial Health

CFA® Exam Overview and Guidelines (Updated for 2021)

Changing Themes (Look and Feel) in ggplot2 in R

Coordinates in ggplot2 in R

Facets for ggplot2 Charts in R (Faceting Layer)

Reader Interactions

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Primary Sidebar

In this Course

  • CFA Level 2: Fixed Income Part 1 – Introduction
  • Principles of Credit Analysis
  • High Yield Corporate Debt (aka Junk bonds)
  • Analyzing Credit of Asset Backed Securities
  • Analyzing Credit of Municipal Bonds
  • Sovereign Debt
  • Three Shapes of the Yield Curve
  • Parallel and Non-parallel Shifts in Yield Curve
  • Factors Driving Treasury Investment Returns and Bond Price Risk
  • Yield Curve Construction with Treasuries
  • LIBOR Swap Rate Curve
  • Theories of the Term Structure of Interest Rates
  • Key Rate Duration
  • How to Calculate Interest Rate Volatility?
  • Benchmark Yield Spreads
  • Valuing an Option Embedded Bond using Binomial Interest Rate Tree
  • How to Price Convertible Bonds?

Latest Tutorials

    • Data Visualization with R
    • Derivatives with R
    • Machine Learning in Finance Using Python
    • Credit Risk Modelling in R
    • Quantitative Trading Strategies in R
    • Financial Time Series Analysis in R
    • VaR Mapping
    • Option Valuation
    • Financial Reporting Standards
    • Fraud
Facebook Group

Membership

Unlock full access to Finance Train and see the entire library of member-only content and resources.

Subscribe

Footer

Recent Posts

  • How to Improve your Financial Health
  • CFA® Exam Overview and Guidelines (Updated for 2021)
  • Changing Themes (Look and Feel) in ggplot2 in R
  • Coordinates in ggplot2 in R
  • Facets for ggplot2 Charts in R (Faceting Layer)

Products

  • Level I Authority for CFA® Exam
  • CFA Level I Practice Questions
  • CFA Level I Mock Exam
  • Level II Question Bank for CFA® Exam
  • PRM Exam 1 Practice Question Bank
  • All Products

Quick Links

  • Privacy Policy
  • Contact Us

CFA Institute does not endorse, promote or warrant the accuracy or quality of Finance Train. CFA® and Chartered Financial Analyst® are registered trademarks owned by CFA Institute.

Copyright © 2021 Finance Train. All rights reserved.

  • About Us
  • Privacy Policy
  • Contact Us