Computational Finance
An efficient adaptive direct numerical integration (DNI) algorithm is developed for computing high quantiles and conditional Value at Risk (CVaR) of compound distributions using characteristic functions. A key innovation of the numerical…
Most previous contributions to BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Using solutions of BSDEs on spaces related to…
Continuous time stochastic processes are useful models especially for financial and insurance purposes. The numerical simulation of such models is dependant of the time discrete discretization, of the parametric estimation and of the choice…
We propose a mathematical framework for the study of a family of random fields--called forward performances--which arise as numerical representation of certain rational preference relations in mathematical finance. Their spatial structure…
For a large class of vanilla contingent claims, we establish an explicit F\"ollmer-Schweizer decomposition when the underlying is a process with independent increments (PII) and an exponential of a PII process. This allows to provide an…
We analyze the problem of the analytical characterization of the probability distribution of financial returns in the exponential Ornstein-Uhlenbeck model with stochastic volatility. In this model the prices are driven by a Geometric…
The problem of existence of solution for the Heath-Jarrow-Morton equation with linear volatility and purely jump random factor is studied. Sufficient conditions for existence and non-existence of the solution in the class of bounded fields…
We consider the exact path sampling of the squared Bessel process and some other continuous-time Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be…
In this paper we are concerned with backward stochastic differential equations with random default time and their applications to default risk. The equations are driven by Brownian motion as well as a mutually independent martingale…
We consider nonparametric estimation of the state price density encapsulated in option prices. Unlike usual density estimation problems, we only observe option prices and their corresponding strike prices rather than samples from the state…
A market with defaultable bonds where the bond dynamics is in a Heath-Jarrow-Morton setting and the forward rates are driven by an infinite number of Levy factors is considered. The setting includes rating migrations driven by a Markov…
This paper adresses the general issue of estimating the sensitivity of the expectation of a random variable with respect to a parameter characterizing its evolution. In finance for example, the sensitivities of the price of a contingent…
We study the performance of the adaptive construction scheme for a Bayesian inference on the Quadratic GARCH model which introduces the asymmetry in time series dynamics. In the adaptive construction scheme a proposal density in the…
We introduce a family of copulas which are locally piecewise uniform in the interior of the unit cube of any given dimension. Within that family, the simultaneous control of tail dependencies of all projections to faces of the cube is…
We propose a method to construct a proposal density for the Metropolis-Hastings algorithm in Markov Chain Monte Carlo (MCMC) simulations of the GARCH model. The proposal density is constructed adaptively by using the data sampled by the…
In this paper we use a hybrid Monte Carlo-Optimal quantization method to approximate the conditional survival probabilities of a firm, given a structural model for its credit defaul, under partial information. We consider the case when the…
An efficient conditioning technique, the so-called Brownian Bridge simulation, has previously been applied to eliminate pricing bias that arises in applications of the standard discrete-time Monte Carlo method to evaluate options written on…
This paper formed part of a preliminary research report for a risk consultancy and academic research. Stochastic Programming models provide a powerful paradigm for decision making under uncertainty. In these models the uncertainties are…
In this paper we show how to relate European call and put options on multiple assets to certain convex bodies called lift zonoids. Based on this, geometric properties can be translated into economic statements and vice versa. For instance,…
We propose a new cognitive framework for option price modelling, using quantum neural computation formalism. Briefly, when we apply a classical nonlinear neural-network learning to a linear quantum Schr\"odinger equation, as a result we get…