In this paper we introduce a discretization scheme based on a continuous-time Markov chain for the Black-Scholes diffusion process. Our principal aim is to find the optimal convergence rate for the probability density function of the discretized process as the distance between the nodes of the...

A mathematical framework for Continuous Time Finance based on operator algebraic methods offers a new direct and entirely constructive perspective on the field. It also leads to new numerical analysis techniques which can take advantage of the emerging massively parallel GPU architectures which...

Although economically more meaningful than the alternatives, short rate models have been dismissed for financial engineering applications in favor of market models as the latter are more flexible and best suited to cluster computing implementations. In this paper, we argue that the paradigm...

This article outlines a framework for the analysis of extreme events based on forward-looking reverse stress testing. We carry out a portfolio simulation and identify stress scenarios which are critical for bank solvency as the ones contributing the most to cost of capital, as expressed by KVA...

Performance assessment of derivative pricing models revolves around a comparative model-risk analysis. From among the plethora of econometrically unrealistic models, the ones that survive Darwinian selection tend to generate systematic short term profits while exposing the bank to long term...

This paper analyses the most widely applied correlation approaches in finance. We first discuss primarily bottom-up approaches, as correlating Brownian motions (Heston 1993), the binomial correlation approach (Lucas 1995), Copulas (Sklar 1959, Li 2000), lattice models with dynamic copulas...

It is a widely recognized fact that risk-reversals play a central role in the pricing of derivatives in foreign exchange markets. It is also known that the values of risk-reversals vary stochastically with time. In this paper we introduce a stochastic volatility model with jumps and local...

In the first quarter of 2006, the Chicago Board Options Exchange introduced, as one of the listed products, options on its implied volatility index (VIX). This created the challenge of developing a pricing framework that can simultaneously handle European options, forward-starts, options on the...