Related papers: Gamma Hedging without Rough Paths

Signatures, one of the key concepts of rough path theory, have recently gained prominence as a means to find appropriate feature sets in machine learning systems. In this paper, in order to compute signatures directly from discrete data…

This paper establishes the existence and uniqueness of solutions for rough differential equations driven by reduced rough paths with low regularity, specifically in the roughness regime $\frac{1}{3} < \alpha \leq \frac{1}{2}$. While the…

Recently, there were works claiming that path integral quantisation of gauge theories necessarily requires relaxation of Lagrangian constraints. As has also been noted in the literature, it is of course wrong since there perfectly exist…

A non-Bayesian, regression-based or generalized least squares (GLS)-based approach is formally proposed to estimate a class of time-varying AR parameter models. This approach has partly been used by Ito et al. (2014, 2016a,b), and is proven…

We propose different schemes for option hedging when asset returns are modeled using a general class of GARCH models. More specifically, we implement local risk minimization and a minimum variance hedge approximation based on an extended…

We characterize absence of arbitrage with simple trading strategies in a discounted market with a constant bond and several risky assets. We show that if there is a simple arbitrage, then there is a 0-admissible one or an obvious one, that…

We consider the classical problem of building an arbitrage-free implied volatility surface from bid-ask quotes. We design a fast numerical procedure, for which we prove the convergence, based on the Sinkhorn algorithm that has been recently…

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…

We introduce a supporting combinatorial framework for the Flat Wall Theorem. In particular, we suggest two variants of the theorem and we introduce a new, more versatile, concept of wall homogeneity as well as the notion of regularity in…

A quantum field theory generalization, Baaquie, of the Heath, Jarrow, and Morton (HJM) term structure model parsimoniously describes the evolution of imperfectly correlated forward rates. Field theory also offers powerful computational…

It is shown that gauge theories are most naturally studied via a polar decomposition of the field variable. Gauge transformations may be viewed as those that leave the density invariant but change the phase variable by additive amounts. The…

We develop the general integral transforms (GIT) method for pricing barrier options in the time-dependent Heston model (also with a time-dependent barrier) where the option price is represented in a semi-analytical form as a two-dimensional…

A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet…

We develop the fundamental theorem of asset pricing in a probability-free infinite-dimensional setup. We replace the usual assumption of a prior probability by a certain continuity property in the state variable. Probabilities enter then…

Many applications require robustness, or ideally invariance, of neural networks to certain transformations of input data. Most commonly, this requirement is addressed by training data augmentation, using adversarial training, or defining…

This paper introduces a transformative framework for managing path-dependent financial risk by shifting from traditional distribution-centric models to a geometry-based approach. We propose the SigSwap as a new regulatory instrument that…

Off-shell supersymmetry, which restricts sparticles to appear only off-shell, solves the gauge hierarchy problem and unifies the gauge couplings in the usual way. Without introducing any new interactions or exacerbating the naturalness,…

In this paper, we first prove that the local time associated with symmetric $\alpha$-stable processes is of bounded $p$-variation for any $p>\frac{2}{\alpha-1}$ partly based on Barlow's estimation of the modulus of the local time of such…

Abstract This paper proposes a novel approach to Bermudan swaption hedging by applying the deep hedging framework to address limitations of traditional arbitrage-free methods. Conventional methods assume ideal conditions, such as zero…

We investigate pricing-hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, e.g. a family of European options, only statically. In the first part of the paper we…