Related papers: A time-stepping deep gradient flow method for opti…

We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model was already described in the literature. We present a new approach to the problem, based on partial…

The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their…

We propose a new approach to quantize the marginals of the discrete Euler diffusion process. The method is built recursively and involves the conditional distribution of the marginals of the discrete Euler process. Analytically, the method…

We consider Heston's (1993) stochastic volatility model for valuation of European options to which (semi) closed form solutions are available and are given in terms of characteristic functions. We prove that the class of scale-parameter…

This paper presents a novel approach to pricing American options using piecewise diffusion Markov processes (PDifMPs), a type of generalised stochastic hybrid system that integrates continuous dynamics with discrete jump processes. Standard…

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…

Sparked by Al\`os, Le\'on, and Vives (2007); Fukasawa (2011, 2017); Gatheral, Jaisson, and Rosenbaum (2018), so-called rough stochastic volatility models such as the rough Bergomi model by Bayer, Friz, and Gatheral (2016) constitute the…

We present a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs, market impact, liquidity constraints or risk limits using modern deep reinforcement machine learning methods. We…

We propose an innovative data-driven option pricing methodology that relies exclusively on the dataset of historical underlying asset prices. While the dataset is rooted in the objective world, option prices are commonly expressed as…

In this paper I develop a new computational method for pricing path dependent options. Using the path integral representation of the option price, I show that in general it is possible to perform analytically a partial averaging over the…

We propose a very efficient method for pricing various types of lookback options under Markov models. We utilize the model-free representations of lookback option prices as integrals of first passage probabilities. We combine efficient…

We price European-style options written on forward contracts in a commodity market, which we model with an infinite-dimensional Heath-Jarrow-Morton (HJM) approach. For this purpose we introduce a new class of state-dependent volatility…

We reinterpret and propose a framework for pricing path-dependent financial derivatives by estimating the full distribution of payoffs using Distributional Reinforcement Learning (DistRL). Unlike traditional methods that focus on expected…

We present a discrete time stochastic volatility model in which the conditional distribution of the logreturns is a Variance-Gamma, that is a normal variance-mean mixture with Gamma mixing density. We assume that the Gamma mixing density is…

In this paper, we propose a machine learning algorithm for time-inconsistent portfolio optimization. The proposed algorithm builds upon neural network based trading schemes, in which the asset allocation at each time point is determined by…

Value functions arise as a component of algorithms as well as performance metrics in statistics and engineering applications. Computation of the associated Bellman equations is numerically challenging in all but a few special cases. A…

This paper proposes to model asset price dynamics with a mixture of diffusion processes where the instantaneous volatility of the underlying diffusion process contains a random vector. The marginal probability distributions of the proposed…

A nonlinear diffusion equation, interpreted as a Wasserstein gradient flow, is numerically solved in one space dimension using a higher-order minimizing movement scheme based on the BDF (backward differentiation formula) discretization. In…

This paper presents a multinomial method for option pricing when the underlying asset follows an exponential Variance Gamma process. The continuous time Variance Gamma process is approximated by a discrete time Markov chain with the same…

We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit…