Mathematician to Rates

Apply your pure mathematics background to fixed income markets and interest rate derivatives. Where stochastic calculus meets real yield curves.

9-12 Months Duration
14 Chapters Core Content
Fixed Income Specialization

Your Mathematical Edge

∫
Stochastic Calculus
Your measure theory and stochastic processes background maps directly to interest rate modeling. Itô calculus becomes the language of yield curve evolution.
→ Short rate models, HJM framework
∂
PDEs
The Black-Scholes equation is a heat equation. Bond pricing follows from Feynman-Kac. Your PDE intuition translates to derivative pricing.
→ Bond option pricing, swaptions
Σ
Linear Algebra
Principal component analysis decomposes yield curve movements. Factor models require eigendecomposition. Matrix exponentials price rate products.
→ PCA of rates, factor hedging
P
Probability Theory
Risk-neutral measure, Girsanov's theorem, change of numeraire. Your probability foundation enables rigorous derivatives pricing.
→ Swap pricing, credit models
THE HEART OF RATES TRADING
dP/P = -D·dr + ½·C·(dr)²
Price-yield relationship. Duration is the first derivative. Convexity is the second. The entire rates business is built on this Taylor expansion.

Curriculum Structure

1
Fixed Income Foundations
Weeks 1-8
Master bond mathematics: pricing, yields, duration, convexity. Build intuition for how interest rate changes affect bond portfolios. This is the grammar of fixed income markets.
Vol I Ch. 6
Bond Pricing
Vol I Ch. 13
Fixed Income Portfolios
2
Yield Curve Models
Weeks 9-18
Construct and calibrate yield curves. Bootstrap from market instruments. Understand forward rates, swap curves, and curve building methodologies. Apply your functional analysis background.
Vol II Ch. 21
Interest Rate Models
Case Study
Swap Curve Construction
3
Rate Derivatives
Weeks 19-32
Price and hedge interest rate swaps, caps, floors, and swaptions. Apply Hull-White, LMM, and SABR models. Your stochastic calculus knowledge applies directly to these pricing problems.
Vol II Ch. 17-18
Options Framework
Case Study
Interest Rate Swaps
Case Study
Callable Range Accrual
4
Trading & Risk
Weeks 33-44
Apply duration and DV01 hedging in practice. Manage curve risk across tenors. Build stress testing frameworks for rate scenarios. Understand the Metallgesellschaft case and liquidity risk.
Vol II Ch. 20
Hedging Strategies
Vol II Ch. 22
Enterprise Risk

Career Outcomes

ENTRY LEVEL
Rates Quant
Build and maintain pricing models for fixed income trading desks. Calibrate curves, implement SABR, support traders.
MID LEVEL
Rates Structurer
Design custom rate products for institutional clients. Price callable bonds, range accruals, structured notes.
MID LEVEL
Risk Manager
Build rate risk frameworks for banks and asset managers. DV01 limits, curve stress testing, regulatory capital.
SENIOR
Rates Portfolio Manager
Run rate strategies at macro funds or fixed income managers. Curve trades, carry strategies, convexity plays.

Apply Your Mathematics

Your abstract algebra and analysis background is the foundation. This path shows you how to apply it to trillion-dollar markets.

Begin Path Derivatives Lab