The Art of Term Structure Models: Volatility and Distribution (FRM Part 2 – Book 1 – Chapter 14)
Build intuition for the Art of Term Structure Models: Volatility and Distribution (FRM Part 2 – Book 1 – Ch. 14). In this lesson we review constant-volatility short-rate models, then introduce time-dependent volatility, mean reversion, and the Cox-Ingersoll-Ross (CIR) framework. We compare basis-point vs lognormal volatility, construct interest-rate trees, and link models to pricing caplets and floorlets. Perfect for FRM candidates who want clear, exam-ready explanations and examples.
What you’ll learn:
Short-term rate process with time-dependent volatility
CIR vs Vasicek; mean reversion and no-negative-rates feature
Basis-point vs lognormal models; Black-Karasinski overview
Building and using interest-rate trees for derivatives pricing
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After completing this reading you should be able to:
Describe the short-term rate process under a model with
time-dependent volatility.
Calculate the short-term rate change and determine the behavior of the
standard deviation of the rate change using a model with time
dependent volatility.
Assess the efficacy of time-dependent volatility models.
Describe the short-term rate process under the Cox-Ingersoll-Ross
(CIR) and lognormal models.
Calculate the short-term rate change and describe the basis point
volatility using the CIR and lognormal models.
Describe lognormal models with deterministic drift and mean reversion.
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