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New Tools to Solve Your Option Pricing Problems For nonlinear PDEs encountered in quantitative finance, advanced probabilistic methods are needed to address dimensionality issues. Written by two leaders in quantitative research--including Risk magazine's 2013 Quant of the Year--Nonlinear Option Pricing compares various numerical methods for solving high-dimensional nonlinear problems arising in option pricing. Designed for practitioners, it is the first authored book to discuss nonlinear Black-Scholes PDEs and compare the efficiency of many different methods. Real-World Solutions for Quantitative Analysts The book helps quants develop both their analytical and numerical expertise. It focuses on general mathematical tools rather than specific financial questions so that readers can easily use the tools to solve their own nonlinear problems. The authors build intuition through numerous real-world examples of numerical implementation. Although the focus is on ideas and numerical examples, the authors introduce relevant mathematical notions and important results and proofs. The book also covers several original approaches, including regression methods and dual methods for pricing chooser options, Monte Carlo approaches for pricing in the uncertain volatility model and the uncertain lapse and mortality model, the Markovian projection method and the particle method for calibrating local stochastic volatility models to market prices of vanilla options with/without stochastic interest rates, the a + b technique for building local correlation models that calibrate to market prices of vanilla options on a basket, and a new stochastic representation of nonlinear PDE solutions based on marked branching diffusions.

Option pricing in a nutshell -- Monte Carlo -- Some excursions in option pricing -- Nonlinear PDEs: a bit of theory -- Examples of nonlinear problems in finance -- Early exercise problems -- Backward stochastic differential equations -- The uncertain lapse and mortality model -- The uncertain volatility model -- McKean nonlinear stochastic differential equations -- Calibration of local stochastic volatility models to market smiles -- Calibration of local correlation models to market smiles -- Marked branching diffusions -- References -- Index

"Given a randomly drawn sample, calibration weighting can provide double protection against the selection bias resulting from unit nonresponse. This means that if either an assumed linear prediction model or an implied unit selection model holds, the resulting estimator will be asymptotically unbiased in some sense. The functional form of the selection model when using linear alibration adjustment is dubious. The authors discuss an alternative, nonlinear calibration-weighting procedure and software that can, among other things, implicitly estimate a logistic-response model." (author's abstract)