Related papers: Discrete LIBOR Market Model Analogy
We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Levy-type martingale subject to default. This class of models allows for local volatility, local default intensity, and a locally dependent…
We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of…
Each training step for a variational autoencoder (VAE) requires us to sample from the approximate posterior, so we usually choose simple (e.g. factorised) approximate posteriors in which sampling is an efficient computation that fully…
In this article we propose a study of market models starting from a set of axioms, as one does in the case of risk measures. We define a market model simply as a mapping from the set of adapted strategies to the set of random variables…
Financial markets exhibit alternating periods of rising and falling prices. Stock traders seeking to make profitable investment decisions have to account for those trends, where the goal is to accurately predict switches from bullish…
The aim of this paper is to develop estimation and inference methods for the drift parameters of multivariate L\'evy-driven continuous-time autoregressive processes of order $p\in\mathbb{N}$. Starting from a continuous-time observation of…
In this article we consider L\'evy driven continuous time moving average processes observed on a lattice, which are stationary time series. We show asymptotic normality of the sample mean, the sample autocovariances and the sample…
It is well known that the Black-Scholes-Merton model suffers from several deficiencies. Jump-diffusion and Levy models have been widely used to partially alleviate some of the biases inherent in this classical model. Unfortunately, the…
Motivated by the convergence result of mirror-descent algorithms to market equilibria in linear Fisher markets, it is natural for one to consider designing dynamics (specifically, iterative algorithms) for agents to arrive at linear…
In this paper we present an algorithm for pricing barrier options in one-dimensional Markov models. The approach rests on the construction of an approximating continuous-time Markov chain that closely follows the dynamics of the given…
We propose a novel time discretization for the log-normal SABR model which is a popular stochastic volatility model that is widely used in financial practice. Our time discretization is a variant of the Euler-Maruyama scheme. We study its…
We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Kr\"uhner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily…
Financial markets are often modelled as if time were unique and continuous across assets and markets. Financial markets are however asynchronous, order flow is event-driven, and waiting times between events are often random. Many of the…
We provide a model-free pricing-hedging duality in continuous time. For a frictionless market consisting of $d$ risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging…
The paper estimates the rate of convergence of the weak Euler approximation for the solutions of SDEs with Hoelder continuous coefficients driven by point and martingale measures. The equation considered has a non-degenerate main part whose…
The objective of the paper is to price weather contracts using temperature as the underlying process when the later follows a mean-reverting dynamics driven by a time-changed Brownian motion coupled to a Gamma Levy subordinator and…
We develop the theory of discrete time Lagrangian mechanics on Lie groups, originated in the work of Veselov and Moser, and the theory of Lagrangian reduction in the discrete time setting. The results thus obtained are applied to the…
We characterise the convergence of a certain class of discrete time Markov processes toward locally Feller processes in terms of convergence of associated operators. The theory of locally Feller processes is applied to L\'evy-type processes…
In this article, we review the construction and properties of some popular approaches to modeling LIBOR rates. We discuss the following frameworks: classical LIBOR market models, forward price models and Markov-functional models. We close…
It is well documented that a model for the underlying asset price process that seeks to capture the behaviour of the market prices of vanilla options needs to exhibit both diffusion and jump features. In this paper we assume that the asset…