The Science of Term Structure Models (FRM Part 2 2025 – Book 1 – Chapter 11)

Master the Science of Term Structure Models for FRM Part 2 (Book 1, Chapter 11). In this lesson you will learn how to build and read binomial interest rate trees, price zero-coupon and option-free bonds with backward induction, use replicating portfolios, switch to risk-neutral probabilities, value constant-maturity swaps, and compute option-adjusted spreads. We also discuss recombining vs non-recombining trees, step size choices, and when Black-Scholes-Merton assumptions break for fixed income.

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After completing this reading you should be able to:
Calculate the expected discounted value of a zero-coupon security using a binomial tree.
Construct and apply an arbitrage argument to price a call option on a zero-coupon security using replicating portfolios.
Define risk-neutral pricing and apply it to option pricing.
Distinguish between true and risk-neutral probabilities, and apply this difference to interest rate drift.
Explain how the principles of arbitrage pricing of derivatives on fixed income securities can be extended over multiple periods.
Define option-adjusted spread (OAS) and apply it to security pricing.
Describe the rationale behind the use of recombining trees in option pricing.
Calculate the value of a constant maturity Treasury swap, given an interest rate tree and the risk-neutral probabilities.
Evaluate the advantages and disadvantages of reducing the size of the time steps on the pricing of derivatives on fixed-income securities.
Evaluate the appropriateness of the Black-Scholes-Merton model when valuing derivatives on fixed income securities.

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