Fixed Income Mathematics: Pricing and Valuation of Bonds

New York Institute of Finance

How long?

  • 2 days
  • in person, online

What are the topics?

New York Institute of Finance

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Who should attend

  • Portfolio managers
  • fixed income traders
  • fixed income desk quants
  • research analysts and financial analysts

About the course

Learn how to determine fair values, yields and risk measures for fixed income securities. The course emphasizes conceptual understanding, but maintains a level of rigor suitable for the development of an effective fixed income toolkit.

This course is a component of the Fixed Income Professional Certificate.

Prerequisite knowledge:

  • Intermediate MS Excel skills
  • Elementary differential calculus
  • Basic probablility and statistics
  • Basic familiarity with fixed income instruments

CURRICULUM

Day 1

MODULE 1: ESSENTIAL MATHEMATICS

  • Geometric series
  • Derivatives
  • Taylor series
  • Logarithmic and exponential functions
  • (Easy) integrals

MODULE 2: BASIC INSTRUMENTS

  • Zero coupon bonds
  • Annuities
  • Perpetuities
  • Coupon Bonds: Bullets and amortizers
  • Par coupon rates
  • Floating rate bonds

MODULE 3: MEASURES OF YIELD AND RETURN

  • Discount rates
  • Yields
  • Interest rates
  • Rates of return: Expected, contractual and realized
  • Yield-to-maturity: What it does and does not mean

Day 2

MODULE 1: TERM STRUCTURES OF RATES AND YIELDS

  • Forward rates
  • Bootstrapping zeros
  • Desirable properties of term structures
  • Interpolation techniques
  • Splines
  • Yield curve fitting

MODULE 2: MEASURES OF RISK

  • Taylor series and 'sensitivity' measures
  • Macaulay duration
  • Yield duration: Macualay and modified
  • Dollar duration
  • Key rate duration
  • Macaulay convexity
  • Yield convexity

MODULE 3: ELEMENTS OF FIXED INCOME PORTFOLIO RISK MANAGEMENT

  • Duration of a portfolio
  • Convexity of a portfolio
  • Immunization
  • Computing Value at Risk for fixed income portfolios

MODULE 4: CORPORATE BONDS

  • Credit risk
  • Inferring (risk-neutral) default probabilities from bond prices

** WHAT YOU'LL LEARN**

  • Understand the 'no-arbitrage' principle employed in the valuation of fixed income securities
  • Understand the limitations of 'yield-to-maturity' as a relative value measure
  • Understand the limitations of 'yield-to-maturity' as a measure of the rate of return on default free fixed income securities
  • Develop a 'no-arbitrage' interpretation of forward rates
  • Develop a deep understanding of duration and convexity and be aware of common misunderstandings of these concepts
  • Understand and be able to reproduce the yield and risk measures on Bloomberg YAS screens for government bonds
  • Derive risk-neutral default probabilities from credit risky bond prices

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Fixed Income Mathematics: Pricing and Valuation of Bonds at New York Institute of Finance

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Full disclaimer.