Related papers: A Path Integral Way to Option Pricing

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 present a novel method for the numerical pricing of American options based on Monte Carlo simulation and the optimization of exercise strategies. Previous solutions to this problem either explicitly or implicitly determine so-called…

In American options, the early exercise feature allows the option to be exercised at any time prior to expiration. However, this flexibility introduces a challenge: the pricing model must value the option while simultaneously determining an…

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…

Following the foundational work of the Black--Scholes model, extensive research has been developed to price the option by addressing its underlying assumptions and associated pricing biases. This study introduces a novel framework for…

We provide a unifying treatment of pathwise moderate deviations for models commonly used in financial applications, and for related integrated functionals. Suitable scaling allows us to transfer these results into small-time, large-time and…

We propose a parameter-free model for estimating the price or valuation of financial derivatives like options, forwards and futures using non-supervised learning networks and Monte Carlo. Although some arbitrage-based pricing formula…

This paper presents a derivation of the explicit price for the perpetual American put option in the Black-Scholes model, time-capped by the first drawdown epoch beyond a predefined level. We demonstrate that the optimal exercise strategy…

We use Lie symmetry methods to price certain types of barrier options. Usually Lie symmetry methods cannot be used to solve the Black-Scholes equation for options because the function defining the maturity condition for an option is not…

The use of random sampling in decision-making and control has become popular with the ease of access to graphic processing units that can generate and calculate multiple random trajectories for real-time robotic applications. In contrast to…

We consider the problem of pricing perpetual American options written on dividend-paying assets whose price dynamics follow a multidimensional Black and Scholes model. For convex Lipschitz continuous reward functions, we give a…

Option pricing is an integral part of modern financial risk management. The well-known Black and Scholes (1973) formula is commonly used for this purpose. This paper is an attempt to extend their work to a situation in which the…

This paper mainly discusses the American option's hedging strategies via binomialmodel and the basic idea of pricing and hedging American option. Although the essential scheme of hedging is almost the same as European option, small…

We introduce and discuss a general criterion for the derivative pricing in the general situation of incomplete markets, we refer to it as the No Almost Sure Arbitrage Principle. This approach is based on the theory of optimal strategy in…

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…

The classical linear Black--Scholes model for pricing derivative securities is a popular model in financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the…

In this work, we study the deep signature algorithms for path-dependent options. We extend the backward scheme in [Hur\'e-Pham-Warin. Mathematics of Computation 89, no. 324 (2020)] for state-dependent FBSDEs with reflections to…

We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial…

In this paper, we give a numerical method for pricing long maturity, path dependent options by using the Markov property for each underlying asset. This enables us to approximate a path dependent option by using some kinds of plain…

We analyze the empirical performance of several non-parametric estimators of the pricing functional for European options, using historical put and call prices on the S&P500 during the year 2012. Two main families of estimators are…