Course Materials
Lecture Notes
Detailed notes for each lecture, covering derivations, definitions, and worked examples. Notes are released alongside each weekly batch.
Bank Account, Discounting, Zero-Coupon Bonds, and Spot Rates
Brigo & Mercurio 1.1–1.2
Foundational discounting objects for the course: money-market account, short rate, discount factor, zero-coupon bond, and spot-rate conventions.
Forward Rates, Swaps, Caps, Floors, and Swaptions
Brigo & Mercurio 1.3–1.6
Forward-looking term-structure objects for the course: zero-coupon curve, forward rates, instantaneous forward rates, swaps, caps, floors, and swaptions.
No-Arbitrage Pricing, Martingale Measures, and Numeraire Change
Brigo & Mercurio 2.1–2.3
Pricing-theoretic foundations for the course: self-financing strategies, no-arbitrage pricing, equivalent martingale measures, contingent claims, and the first numeraire-change toolkit.
Forward Measures
Brigo & Mercurio Sections 2.3.1–2.6.1
Completing the numeraire-change toolkit: drift corrections, diffusion-coefficient notation, convenient numeraires, the T-forward measure, and fundamental pricing formulas.
Deferred Payoffs
Brigo & Mercurio Sections 2.6.1–2.9
Closing the no-arbitrage chapter: caplets as zero-coupon bond options, deferred payoff valuation, multiple-payment claims under a terminal measure, and foreign-market numeraire change.
Vasicek Model
Brigo & Mercurio Sections 3.1–3.2.1
Beginning the modeling chapter: one-factor short-rate dynamics, risk-neutral versus objective measures, Vasicek mean reversion, affine bond pricing, bond options, and AR(1) estimation.
Dothan, CIR, and EV
Brigo & Mercurio Sections 3.2.2–3.2.5
Continuing classical one-factor short-rate models: Dothan lognormal rates, CIR square-root diffusion, affine term-structure structure, Exponential Vasicek, positivity, mean reversion, tractability, and model-selection tradeoffs.
Hull–White Model
Brigo & Mercurio Section 3.3
Studying the Hull–White extended Vasicek model: time-dependent drift, exact initial curve fitting, affine bond pricing, zero-coupon bond options, caps and floors, Jamshidian’s decomposition, trinomial tree construction, Arrow–Debreu prices, and discrete curve calibration.