In this chapter we study the problem of valuing a (possibly defaultable) derivative asset
contingent on the underlying economic state modeled as a Markov process. To gain …

We solve a model with two iid Lucas trees. Although the corresponding one-tree model
produces a constant price-dividend ratio and iid returns, the two-tree model produces …

Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing is the
first book that applies advanced analytical and geometrical methods used in physics and …

This paper develops a spectral expansion approach to the valuation of contingent claims
when the underlying state variable follows a one-dimensional diffusion with the infinitesimal …

In this paper, we derive a general asymptotic implied volatility at the first-order for any
stochastic volatility model using the heat kernel expansion on a Riemann manifold endowed …

This is a book on financial modeling that emphasizes computational aspects. It gives a
unified perspective on derivative pricing and hedging across asset classes and is addressed …

Using Malliavin calculus techniques, we derive an analytical formula for the price of
European options, for any model including local volatility and Poisson jump processes. We …

This paper develops a spectral theory of Markovian asset pricing models where the
underlying economic uncertainty follows a continuous-time Markov process X with a general …

Advanced Derivatives Pricing and Risk Management covers the most important and cutting-
edge topics in financial derivatives pricing and risk management, striking a fine balance …

Stochastic volatility (SV) and local stochastic volatility (LSV) processes can be used to model
the evolution of various financial variables such as FX rates, stock prices and so on …