Model Calibration
Nonlinear least-squares fitting of stochastic volatility and interest rate models to market quotes: Levenberg-Marquardt and trust-region methods for Heston and SABR, LMM swaption calibration, Jacobian computation via finite difference and AAD, and convergence diagnostics used on a live pricing desk.
5 modules~135 min total
Prerequisites
Vol Surface ParametrisationImplied Vol InversionLinear Algebra & Matrix Methods (SVD, least squares)
Modules
01
Model Calibration as a Non-Linear Least Squares Problem
MediumNon-Linear Least SquaresCalibration ObjectiveResidual VectorJacobianGauss-Newton
02
The Levenberg-Marquardt Algorithm — Theory and Implementation
HardLevenberg-MarquardtTrust RegionDamping ParameterGauss-NewtonConvergence
03
Jacobian Computation — Finite Difference and AAD
HardJacobianFinite DifferencesComplex StepAADAutomatic Differentiation
04
Heston Model Calibration in Practice — Fitting the Smile
HardHeston ModelCharacteristic FunctionLewis FormulaCalibrationImplied Volatility Surface
05
SABR and LMM Calibration — Multi-Instrument Fitting
HardSABR CalibrationLMMSwaption CubeRank ReductionCascade Calibration