This book is mainly devoted to finite difference numerical methods for solving partial differential equations (PDEs) models of pricing a wide variety of financial derivative securities. With this objective, the book is divided into two main parts.

In the first part, after an introduction concerning the basics on derivative securities, the authors explain how to establish the adequate PDE boundary value problems for different sets of derivative products (vanilla and exotic options, and interest rate derivatives). For many option problems, the analytic solutions are also derived with...

Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure...

Backward stochastic differential equations (BSDEs) provide a general mathematical framework for solving pricing and risk management questions of financial derivatives. They are of growing importance for nonlinear pricing problems such as CVA computations that have been developed since the crisis. Although BSDEs are well known to academics, they are less familiar to practitioners in the financial industry. In order to fill this gap, this book revisits financial modeling and computational finance from a BSDE perspective, presenting a unified view of the pricing and hedging theory across all...

Fixed income volatility and equity volatility evolve heterogeneously over time, co-moving disproportionately during periods of global imbalances and each reacting to events of different nature. While the methodology for options-based "model-free" pricing of equity volatility has been known for some time, little is known about analogous methodologies for pricing various fixed income volatilities.

This book fills this gap and provides a unified evaluation framework of fixed income volatility while dealing with disparate markets such as interest-rate swaps, government bonds,...

This book explains how Interest-rate models work and shows how to implement them for concrete pricing. The revised 2nd edition of this book incorporates considerable new material, including sections on local-volatility dynamics, and on stochastic volatility models.