Related papers: Hedging option books using neural-SDE market model…
In this article, we tackle the problem of a market maker in charge of a book of options on a single liquid underlying asset. By using an approximation of the portfolio in terms of its vega, we show that the seemingly high-dimensional…
The mean-variance hedging (MVH) problem is studied in a partially observable market where the drift processes can only be inferred through the observation of asset or index processes. Although most of the literatures treat the MVH problem…
It is critical yet challenging for deep learning models to properly characterize uncertainty that is pervasive in real-world environments. Although a lot of efforts have been made, such as heteroscedastic neural networks (HNNs), little work…
We construct an aggregator for a family of Snell envelopes in a nondominated framework. We apply this construction to establish a robust hedging duality, along with the existence of a minimal hedging strategy, in a general semi-martingale…
As soon as one accepts to abandon the zero-risk paradigm of Black-Scholes, very interesting issues concerning risk control arise because different definitions of the risk become unequivalent. Optimal hedges then depend on the quantity one…
Paper is based on "The cost of illiquidity and its effects on hedging", L. C. G. Rogers and Surbjeet Singh, 2010. We generalize its thesis to constant elasticity model, which own previously used Black-Schoels model as a special case. The…
We study the SAM (Sharpness-Aware Minimization) optimizer which has recently attracted a lot of interest due to its increased performance over more classical variants of stochastic gradient descent. Our main contribution is the derivation…
We investigate neural ordinary and stochastic differential equations (neural ODEs and SDEs) to model stochastic dynamics in fully and partially observed environments within a model-based reinforcement learning (RL) framework. Through a…
Model risk arises from the misspecification of probabilistic models used for pricing and hedging derivatives. While model risk for European-style claims has been widely studied, much less attention has been given to American-style…
This paper is concerned with the study of insurance related derivatives on financial markets that are based on non-tradable underlyings, but are correlated with tradable assets. We calculate exponential utility-based indifference prices,…
Standard methods and theories in finance can be ill-equipped to capture highly non-linear interactions in financial prediction problems based on large-scale datasets, with deep learning offering a way to gain insights into correlations in…
This paper presents a new model for options pricing. The Black-Scholes-Merton (BSM) model plays an important role in financial options pricing. However, the BSM model assumes that the risk-free interest rate, volatility, and equity premium…
In incomplete financial markets, pricing and hedging European options lack a unique no-arbitrage solution due to unhedgeable risks. This paper introduces a constrained deep learning approach to determine option prices and hedging strategies…
We introduce a new approach for generating sequences of implied volatility (IV) surfaces across multiple assets that is faithful to historical prices. We do so using a combination of functional data analysis and neural stochastic…
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…
Using a combination of recurrent neural networks and signature methods from the rough paths theory we design efficient algorithms for solving parametric families of path dependent partial differential equations (PPDEs) that arise in pricing…
Option pricing often requires solving partial differential equations (PDEs). Although deep learning-based PDE solvers have recently emerged as quick solutions to this problem, their empirical and quantitative accuracy remain not well…
Parametric estimation of stochastic differential equations (SDEs) has been a subject of intense studies already for several decades. The Heston model for instance is driven by two coupled SDEs and is often used in financial mathematics for…
We consider the performance of non-optimal hedging strategies in exponential L\'evy models. Given that both the payoff of the contingent claim and the hedging strategy admit suitable integral representations, we use the Laplace transform…
In the paper we develop mathematical tools of quantile hedging in incomplete market. Those could be used for two significant applications: o calculating the \textbf{optimal capital requirement imposed by Solvency II} (Directive 2009/138/EC…