Interest Rate Modeling

Yield Curve and Its 6 Representations
Girsanov’s Theorem and the Change of Numeraire Formula
- Shreve’s Theorem 9.2.1 and 9.2.2
Interest Rate Swaps and Vanilla Options Pricing
- Swaps
  - Yield Curve Construction
- Caps and Floors
- Swaptions
- Black Normal Model, SABR Model, and Swaption Grid
The HJM Framework
- Derivation
- Dynamics of \(L\) (LIBOR)
  - Instantaneous Forward Rate Vol and Skew
  - Forward Future Convexity Adjustment
- Dynamics of \(S\)
- Duration and HJM
- SOFR Extension
  - Extended Hexagon
  - Dynamics of \(L\) and Cap Pricing
  - SABR RFR
  - Forward Future Convexity Adjustment
HW1F
- Separable Vol and Markovian Short Rate
- Time Stationary Vol and Vol Hump
- Jamshidian for Swaption Pricing
- Bermudan Swaption
LIBOR Market Model
- Spot Measure
- Discrete HJM
Mid-Curve Swaption Pricing
CMS Caps and CMS Spread Options
- Break Even CMS Rate
- CMS Convexity Adjustment
- Annuity Mapping Function
- Replication Method
- Distribution of \(S_T\) in the \(T_p\)-Forward Measure
- Copula Models for CMS Spread Option Pricing
HW2F
- Covariance Structure in the Multi-Dimensional HJM Model
- Separable Vol and Markovian Short Rate
- Time Stationary Vol and Vol Hump
- Jamshidian for Swaption Pricing
Multi-Factor Cheyette Model
- Leif Andersen Parameterization
- Swaption Grid Revisited
  - Limiting Swap Curve
Other Topics
- Curve PCA
  - Variance Explained
  - PnL Attribution
  - HW2F Implied PCs
- Nelson Siegel
- MPCA
- Event Weight
- Longstaff Schwartz