Related papers: Differential Machine Learning for 0DTE Options wit…
We propose methods to infer jumps of a semi-martingale, which describes long-term price dynamics, based on discrete, noisy, high-frequency observations. Different to the classical model of additive, centered market microstructure noise, we…
Neural networks with sufficiently smooth activation functions can approximate values and derivatives of any smooth function, and they are differentiable themselves. We improve the approximation capability of neural networks by utilizing the…
In this paper we propose an efficient method to compute the price of multi-asset American options, based on Machine Learning, Monte Carlo simulations and variance reduction technique. Specifically, the options we consider are written on a…
In this article, we provide representations of European and American exchange option prices under stochastic volatility jump-diffusion (SVJD) dynamics following models by Merton (1976), Heston (1993), and Bates (1996). A Radon-Nikodym…
The Black-Scholes option pricing model remains a cornerstone in financial mathematics, yet its application is often challenged by the need for accurate hedging strategies, especially in dynamic market environments. This paper presents a…
In the first part of this thesis, we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic…
In the present paper we present a finite element approach for option pricing in the framework of a well-known stochastic volatility model with jumps, the Bates model. In this model the asset log-returns are assumed to follow a…
We present an algorithm for the calibration of local volatility from market option prices through deep self-consistent learning, by approximating both market option prices and local volatility using deep neural networks. Our method uses the…
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving…
We consider a method of lines (MOL) approach to determine prices of European and American exchange options when underlying asset prices are modelled with stochastic volatility and jump-diffusion dynamics. As the MOL, as with any other…
This paper presents the solution to a European option pricing problem by considering a regime-switching jump diffusion model of the underlying financial asset price dynamics. The regimes are assumed to be the results of an observed pure…
We consider option hedging in a model where the underlying follows an exponential L\'evy process. We derive approximations to the variance-optimal and to some suboptimal strategies as well as to their mean squared hedging errors. The…
In this article, we investigate the behavior of long-term options. In many cases, option prices follow an exponential decay (or growth) rate for further maturity dates. We determine under what conditions option prices are characterized by…
We consider off-policy evaluation (OPE) in continuous treatment settings, such as personalized dose-finding. In OPE, one aims to estimate the mean outcome under a new treatment decision rule using historical data generated by a different…
This work examines a stochastic volatility model with double-exponential jumps in the context of option pricing. The model has been considered in previous research articles, but no thorough analysis has been conducted to study its quality…
We present an adaptive approach for valuing the European call option on assets with stochastic volatility. The essential feature of the method is a reduction of uncertainty in latent volatility due to a Bayesian learning procedure. Starting…
We propose analytical approximations for the sensitivities (Greeks) of the Asian options in the Black-Scholes model, following from a small maturity/volatility approximation for the option prices which has the exact short maturity limit,…
We develop and study stability properties of a hybrid approximation of functionals of the Bates jump model with stochastic interest rate that uses a tree method in the direction of the volatility and the interest rate and a…
Since the introduction of the Black-Scholes model stochastic processes have played an increasingly important role in mathematical finance. In many cases prices, volatility and other quantities can be modeled using stochastic ordinary…
We introduce a new probabilistic method for solving a class of impulse control problems based on their representations as Backward Stochastic Differential Equations (BSDEs for short) with constrained jumps. As an example, our method is used…