Related papers: Option Pricing via Multi-path Autoregressive Monte…
In this paper we introduce a new approach to model-free path-dependent option pricing. We first introduce a general duality result for linear optimisation problems over signed measures introduced in [3] and show how the the problem of…
In this paper we propose and analyse a method for estimating three quantities related to an Asian option: the fair price, the cumulative distribution function, and the probability density. The method involves preintegration with respect to…
The Black-Scholes theory of option pricing has been considered for many years as an important but very approximate zeroth-order description of actual market behavior. We generalize the functional form of the diffusion of these systems and…
We develop a theory for option pricing with perfect hedging in an inefficient market model where the underlying price variations are autocorrelated over a time tau. This is accomplished by assuming that the underlying noise in the system is…
A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…
The quasi-Monte Carlo method is widely used in computational finance, whose efficiency strongly depends on the smoothness and effective dimension of the integrand. In this work, we investigate the combination of importance sampling and the…
We investigate the approximation of path functionals. In particular, we advocate the use of the Karhunen-Lo\`eve expansion, the continuous analogue of Principal Component Analysis, to extract relevant information from the image of a…
In this paper, we address a method that integrates reinforcement learning into the Monte Carlo tree search to boost online path planning under fully observable environments for automated parking tasks. Sampling-based planning methods under…
The present article explores the application of randomized control techniques in empirical asset pricing and performance evaluation. It introduces geometric random walks, a class of Markov chain Monte Carlo methods, to construct flexible…
This article addresses the problem of approximating the price of options on discrete and continuous arithmetic average of the underlying, i.e. discretely and continuously monitored Asian options, in local volatility models. A…
The valuation of over-the-counter derivatives is subject to a series of valuation adjustments known as xVA, which pose additional risks for financial institutions. Associated risk measures, such as the value-at-risk of an underlying…
Employing probabilistic techniques we compute best possible upper and lower bounds on the price of an option on one or two assets with continuous piecewise linear payoff function based on prices of simple call options of possibly distinct…
We propose three different data-driven approaches for pricing European-style call options using supervised machine-learning algorithms. These approaches yield models that give a range of fair prices instead of a single price point. The…
In this article, we propose a new numerical approach to high-dimensional partial differential equations (PDEs) arising in the valuation of exotic derivative securities. The proposed method is extended from Reisinger and Wittum (2007) and…
We apply path integration techniques to obtain option pricing with stochastic volatility using a generalized Black-Scholes equation known as the Merton and Garman equation. We numerically simulate the option prices using the technique of…
We develop several deep learning algorithms for approximating families of parametric PDE solutions. The proposed algorithms approximate solutions together with their gradients, which in the context of mathematical finance means that the…
A long-standing issue in mathematical finance is the speed-up of option pricing, especially for multi-asset options. A recent study has proposed to use tensor train learning algorithms to speed up Fourier transform (FT)-based option…
We consider a discrete-time approximation of paths of an Ornstein--Uhlenbeck process as a mean for estimation of a price of European call option in the model of financial market with stochastic volatility. The Euler--Maruyama approximation…
We show how Adjoint Algorithmic Differentiation (AAD) allows an extremely efficient calculation of correlation Risk of option prices computed with Monte Carlo simulations. A key point in the construction is the use of binning to…
A critical problem in the financial world deals with the management of risk, from regulatory risk to portfolio risk. Many such problems involve the analysis of securities modelled by complex dynamics that cannot be captured analytically,…