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The Heston stochastic volatility model is a widely used tool in financial mathematics for pricing European options. However, its calibration remains computationally intensive and sensitive to local minima due to the model's nonlinear…
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 investigates the deep hedging framework, based on reinforcement learning (RL), for the dynamic hedging of swaptions, contrasting its performance with traditional sensitivity-based rho-hedging. We design agents under three…
Quantum machine learning has the potential for a transformative impact across industry sectors and in particular in finance. In our work we look at the problem of hedging where deep reinforcement learning offers a powerful framework for…
An investor faced with a contingent claim may eliminate risk by perfect hedging, but as it is often quite expensive, he seeks partial hedging (quantile hedging or efficient hedging) that requires less capital and reduces the risk. Efficient…
We investigate the use of path signatures in a machine learning context for hedging exotic derivatives under non-Markovian stochastic volatility models. In a deep learning setting, we use signatures as features in feedforward neural…
The standard Black-Scholes theory of option pricing is extended to cope with underlying return fluctuations described by general probability distributions. A Langevin process and its related Fokker-Planck equation are devised to model the…
We present an actor-critic-type reinforcement learning algorithm for solving the problem of hedging a portfolio of financial instruments such as securities and over-the-counter derivatives using purely historic data. The key characteristics…
Differential equations can be used to construct predictive models of a diverse set of real-world phenomena like heat transfer, predator-prey interactions, and missile tracking. In our work, we explore one particular application of…
We study the capability of arbitrage-free neural-SDE market models to yield effective strategies for hedging options. In particular, we derive sensitivity-based and minimum-variance-based hedging strategies using these models and examine…
In recent decades, companies have frequently adopted share repurchase programs to return capital to shareholders or for other strategic purposes, instructing investment banks to rapidly buy back shares on their behalf. When the executing…
The approach that allows find European option price on the assumption of hedging at discrete times is proposed. The routine allows find the option price not for lognormal distribution functions of underlying asset only but for wide enough…
This article introduces the groundbreaking concept of the financial differential machine learning algorithm through a rigorous mathematical framework. Diverging from existing literature on financial machine learning, the work highlights the…
This article considers the pricing and hedging of a call option when liquidity matters, that is, either for a large nominal or for an illiquid underlying asset. In practice, as opposed to the classical assumptions of a price-taking agent in…
In this article, we introduce an algorithm called Backward Hedging, designed for hedging European and American options while considering transaction costs. The optimal strategy is determined by minimizing an appropriate loss function, which…
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…
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…
Straddle Option is a financial trading tool that explores volatility premiums in high-volatility markets without predicting price direction. Although deep reinforcement learning has emerged as a powerful approach to trading automation in…
A new method for stochastic control based on neural networks and using randomisation of discrete random variables is proposed and applied to optimal stopping time problems. The method models directly the policy and does not need the…
This paper proposes a two-phase deep reinforcement learning approach, for hedging variable annuity contracts with both GMMB and GMDB riders, which can address model miscalibration in Black-Scholes financial and constant force of mortality…