# Fixed Income Mathematics: Pricing and Valuation of Bonds

## 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 desk quants
• research analysts and financial analysts

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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