Day 1

Basics
and
Calibration

• Why market models and theoretical underpinnings.
• Achieving a speedy Monte Carlo implementation: drift computation, drift approximation, accelerating convergence, latest implementations of Sobol
• QuantLib classes: MarketModelEvolver, LogNormalFwdRatePc, LogNormalFwdRateIpc, LogNormalCotSwapRatePc, LMMDriftCalculator, NormalFwdRatePc, BrownianGenerator, SobolRsg
• Calibration: time homogeneity, correlation structures, the pseudo-square root as a fundamental building block, stable simultaneous calibration to caplets and swaptions, period mismatches,
• QuantLib classes: MarketModel, SwapForwardMappings, FwdToCotSwapAdapter, CotSwapToFwdAdapter, PiecewiseConstantAbcdVariance, CTSMMCapletCalibration, CTSMMCapletMaxHomogeneityCalibration, capletSwaptionPeriodicCalibration

Day 2

Early
Exercise
and
Greeks

• Pricing products with early exercise features, obtaining lower bounds. Least-squares method. Anderson’s method. Orthogonalization,
• QuantLib classes: NodeData, collectNodeData, MarketModelExerciseValue, LongstaffSchwartzExerciseStrategy, MarketModelBasisSystem, MarketModelParametricExercise, genericLongstaffSchwartzRegression
• Upper bounds for callable products.
• QuantLib classes: UpperBoundEngine
• Greek computation: partial proxy simulation and the conditional analytic method.
• QuantLib classes: ConstrainedEvolver, LogNormalFwdRateEulerConstrained

Day 3

Skew
and
Smiles

• Using displaced diffusion to achieve skew
• QuantLib classes: how existing classes already include Displaced Diffusion
• Using Heston stochastic volatility to obtain smile: Monte Carlo implementation
• QuantLib classes: adding an extra evolver to implement stochastic volatility
• Analytic approximations of the stochastic vol LMM, calibration, SABR and the LMM
• QuantLib classes: possible ways to extend to encompass these cases