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Options have provided a field of much study because of the complexity involved in pricing them. The Black-Scholes equations were developed to price options but they are only valid for European styled options. There is added complexity when…

Computational Engineering, Finance, and Science · Computer Science 2007-05-23 Michael Maio Pires , Tshilidzi Marwala

Deep hedging represents a cutting-edge approach to risk management for financial derivatives by leveraging the power of deep learning. However, existing methods often face challenges related to computational inefficiency, sensitivity to…

Machine Learning · Computer Science 2025-02-26 Lei Zhao , Lin Cai

This research addresses accurate option pricing by employing models beyond the traditional Black-Scholes framework. While Black-Scholes provides a closed-form solution, it is limited by assumptions of constant volatility, no dividends, and…

Computational Finance · Quantitative Finance 2026-04-08 Karmanpartap Singh Sidhu , Pranshi Saxena

An option market maker incurs funding costs when carrying and hedging inventory. To hedge a net long delta inventory, for example, she pays a fee to borrow stock from the securities lending market. Because of haircuts, she posts additional…

Pricing of Securities · Quantitative Finance 2020-05-05 Wujiang Lou

This work studies the deep learning-based numerical algorithms for optimal hedging problems in markets with general convex transaction costs on the trading rates, focusing on their scalability of trading time horizon. Based on the…

Mathematical Finance · Quantitative Finance 2022-12-29 Xiaofei Shi , Daran Xu , Zhanhao Zhang

While time series momentum is a well-studied phenomenon in finance, common strategies require the explicit definition of both a trend estimator and a position sizing rule. In this paper, we introduce Deep Momentum Networks -- a hybrid…

Machine Learning · Statistics 2020-09-29 Bryan Lim , Stefan Zohren , Stephen Roberts

This study investigates the application of machine learning techniques, specifically Neural Networks, Random Forests, and CatBoost for option pricing, in comparison to traditional models such as Black-Scholes and Heston Model. Using both…

Computational Finance · Quantitative Finance 2025-10-03 Georgy Milyushkov

Dynamic hedging is a financial strategy that consists in periodically transacting one or multiple financial assets to offset the risk associated with a correlated liability. Deep Reinforcement Learning (DRL) algorithms have been used to…

Computational Finance · Quantitative Finance 2025-04-18 Andrei Neagu , Frédéric Godin , Leila Kosseim

Deep hedging is a deep-learning-based framework for derivative hedging in incomplete markets. The advantage of deep hedging lies in its ability to handle various realistic market conditions, such as market frictions, which are challenging…

Computational Finance · Quantitative Finance 2023-07-26 Masanori Hirano , Kentaro Minami , Kentaro Imajo

We develop deep learning models to learn the hedge ratio for S&P500 index options directly from options data. We compare different combinations of features and show that a feedforward neural network model with time to maturity,…

Statistical Finance · Quantitative Finance 2021-11-08 Jie Chen , Lingfei Li

In this work we deal with the funding costs rising from hedging the risky securities underlying a target volatility strategy (TVS), a portfolio of risky assets and a risk-free one dynamically rebalanced in order to keep the realized…

Pricing of Securities · Quantitative Finance 2021-12-06 Roberto Daluiso , Emanuele Nastasi , Andrea Pallavicini , Stefano Polo

We present a numerically efficient approach for learning a risk-neutral measure for paths of simulated spot and option prices up to a finite horizon under convex transaction costs and convex trading constraints. This approach can then be…

Computational Finance · Quantitative Finance 2021-07-15 Hans Buehler , Phillip Murray , Mikko S. Pakkanen , Ben Wood

Option pricing in real markets faces fundamental challenges. The Black--Scholes--Merton (BSM) model assumes constant volatility and uses a linear generator $g(t,x,y,z)=-ry$, while lacking explicit behavioral factors, resulting in systematic…

Computational Finance · Quantitative Finance 2026-01-28 Yilun Zhang , Zheng Tang , Hexiang Sun , Yufeng Shi

In this paper we introduce a deep learning method for pricing and hedging American-style options. It first computes a candidate optimal stopping policy. From there it derives a lower bound for the price. Then it calculates an upper bound, a…

Computational Finance · Quantitative Finance 2021-03-23 Sebastian Becker , Patrick Cheridito , Arnulf Jentzen

One of the most discussed problems in the financial world is stock option pricing. The Black-Scholes Equation is a Parabolic Partial Differential Equation which provides an option pricing model. The present work proposes an approach based…

Machine Learning · Computer Science 2024-05-12 Daniel de Souza Santos , Tiago Alessandro Espinola Ferreira

This paper contributes to the existing literature on hedging American options with Deep Reinforcement Learning (DRL). The study first investigates hyperparameter impact on hedging performance, considering learning rates, training episodes,…

Risk Management · Quantitative Finance 2024-05-15 Reilly Pickard , F. Wredenhagen , Y. Lawryshyn

The key objective of this paper is to develop an empirical model for pricing SPX options that can be simulated over future paths of the SPX. To accomplish this, we formulate and rigorously evaluate several statistical models, including…

Pricing of Securities · Quantitative Finance 2025-06-24 Alessio Brini , David A. Hsieh , Patrick Kuiper , Sean Moushegian , David Ye

Stochastic differential equation (SDE) models are the foundation for pricing and hedging financial derivatives. The drift and volatility functions in SDE models are typically chosen to be algebraic functions with a small number (less than…

Computational Finance · Quantitative Finance 2024-06-04 Lei Fan , Justin Sirignano

American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale…

Pricing of Securities · Quantitative Finance 2008-12-02 Alet Roux , Tomasz Zastawniak

This study deals with the problem of pricing European currency options in discrete time setting, whose prices follow the fractional Black Scholes model with transaction costs. Both the pricing formula and the fractional partial differential…

Pricing of Securities · Quantitative Finance 2018-05-03 Foad Shokrollahi