Options & Derivatives Pricing

In this work, we study the pricing of American options under stochastic local volatility (SLV) models extended by including stochastic correlation driven by an additional stochastic process. We generalize the class of SLV models by incorporating a flexible stochastic correlation structure. To price

Building on the forest expansion of Alòs, Gatheral and Radoičić and on the explicit Bergomi-Guyon smile expansion derived by Bourgey and Gatheral (2026), we derive fixed-point approximations, in terms of the implied total variance at a small number of magic strikes, for the fair values of power payo

We provide a model for the nested optimisation problem of market making and rebate design problems in option markets and find optimal strategies. A single market maker trades multiple European call options in a local-stochastic volatility option market with both make and take strategies, modeled, re

We examine the conditional volatility dynamics of the USD 1Yx10Y forward swap rate using GARCH(1,1), GJR-GARCH(1,1), and a two-regime Markov-switching GARCH (MSGARCH) model. The analysis uses daily data from 2007 to 2023 and incorporates market-implied measures (ATM swaption volatility and the SRVIX

This paper proposes a hybrid methodology to improve the approximation of SABR (Stochastic Alpha Beta Rho) implied volatility by combining analytical structure with machine learning. The approach augments the neural-network input representation with geometric features derived from the stochastic diff

We study permissionless spot–perpetual basis trading in decentralized finance as a collateral control problem. The strategy holds spot inventory, hedges directional exposure with a short perpetual, and allocates capital between spot inventory and derivative margin under on-chain liquidity and execu

Generating realistic synthetic option prices requires implied volatility as an input, yet implied volatility is itself derived from observed option prices, creating a circular dependency that limits synthetic data for machine-learning and risk-analysis applications. We break this circularity with a

We derive the stochastic price process for tokens whose sole price discovery mechanism is a constant-product automated market maker (AMM). When the net flow into the pool follows a diffusion, the token price follows a constant elasticity of variance (CEV) process, nesting Black-Scholes as the limiti

The estimation of the Risk Neutral Density (RND) implicit in option prices is challenging, especially in illiquid markets. We introduce the Deep Log-Sum-Exp Neural Network, an architecture that leverages Deep and Transfer learning to address RND estimation in the presence of irregular and illiquid s

We introduce a novel signature approach for pricing and hedging path-dependent options with instantaneous and permanent market impact under a mean-quadratic variation criterion. Leveraging the expressive power of signatures, we recast an inherently nonlinear and non-Markovian stochastic control prob

This paper proposes the Exact Terminal Condition Neural Network (ETCNN), a deep learning framework for accurately pricing American options by solving the Black-Scholes-Merton (BSM) equations. The ETCNN incorporates carefully designed functions that ensure the numerical solution not only exactly sati

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 synthetically generated data and real market option data, each

We explore the performance of various artificial neural network architectures, including a multilayer perceptron (MLP), Kolmogorov-Arnold network (KAN), LSTM-GRU hybrid recursive neural network (RNN) models, and a time-delay neural network (TDNN) for pricing European call options. In this study, we

This paper addresses the problem of pricing involved financial derivatives by means of advanced of deep learning techniques. More precisely, we smartly combine several sophisticated neural network-based concepts like differential machine learning, Monte Carlo simulation-like training samples and joi

In this study, we examine the fluctuation in the value of the Great Britain Pound (GBP). We focus particularly on its relationship with the United States Dollar (USD) and the Euro (EUR) currency pairs. Utilizing data from June 15, 2018, to June 15, 2023, we apply various mathematical models to asses

Option contracts on two underlying assets within uncertain volatility models have their worst-case and best-case prices determined by a two-dimensional (2D) Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE) with cross-derivative terms. This paper introduces a novel ``decompose and in

Option pricing, a fundamental problem in finance, often requires solving non-linear partial differential equations (PDEs). When dealing with multi-asset options, such as rainbow options, these PDEs become high-dimensional, leading to challenges posed by the curse of dimensionality. While deep learni

Stochastic volatility models, where the volatility is a stochastic process, can capture most of the essential stylized facts of implied volatility surfaces and give more realistic dynamics of the volatility smile/skew. However, they come with the significant issue that they take too long to calibrat

We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions of investment vehicles such as hedge funds. However, a majo

In this paper, we present a randomized extension of the deep splitting algorithm introduced in [Beck, Becker, Cheridito, Jentzen, and Neufeld (2021)] using random neural networks suitable to approximately solve both high-dimensional nonlinear parabolic PDEs and PIDEs with jumps having (possibly) inf