Exponential Lévy processes can be used to model the evolution of various financial variables such as FX rates, stock prices, etc. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such processes, and the corresponding implied volatility surfaces...

We describe a new framework for collateralized exposure modelling under an ISDA Master Agreement with a Credit Support Annex. The proposed model captures legal and operational aspects of default in considerably greater detail than models currently used by most practitioners, while remaining...

This objective of this paper is to develop a generic, yet practical framework for construction of Markov models for commodity derivatives. We aim for sufficient richness to permit applications to a broad variety of commodity markets, including those that are characterized by seasonality and by...

This paper considers the pricing of European options on assets that follow a stochastic differential equation with a quadratic volatility term. We correct errors in the existing literature, extend the pricing formulas to arbitrary root configurations, and list alternative representations of...

Stochastic volatility models are increasingly important in practical derivatives pricing applications, yet relatively little work has been undertaken in the development of practical Monte Carlo simulation methods for this class of models. This paper considers several new algorithms for...

Polynomial splines are popular in the estimation of discount bond term structures, but suffer from well-documented problems with spurious inflection points, excessive convexity, and lack of locality in the effects of input price perturbations. In this paper, we address these issues through the...

In this paper, we demonstrate that many stochastic volatility models have the undesirable property that moments of order higher than one can become infinite in finite time. As arbitrage-free price computation for a number of important fixed income products involves forming expectations of...

We leverage the new framework for collateralized exposure modelling in Andersen, Pykhtin, and Sokol (2016) to analyze credit risk on positions collateralized with both variation and initial margin. Special attention is paid to the dynamic BCBS-IOSCO uncleared margin rules soon to be mandated for...

We demonstrate that the funding value adjustments (FVAs) of major dealers are debt-overhang costs to their shareholders. In order to maximize shareholder value, dealer quotations therefore adjust for FVAs. Contrary to current valuation practice, FVAs are not themselves components of the market...

We develop a new high-performance spectral collocation method for the computation of American put and call option prices. The proposed algorithm involves a carefully posed Jacobi-Newton iteration for the optimal exercise boundary, aided by Gauss-Legendre quadrature and Chebyshev polynomial...