arXiv · arXiv q-fin · 2026
We consider a generalization of the variance-gamma (generalized asymmetric Laplace) distribution, defined as a normal mean - variance mixture with a gamma mixing distribution. While this model is typically studied in the univariate setting, we assume that the gamma mixing variable is observed alongside the primary variable, resulting in a bivariate framework. In this setting, maximum likelihood estimation becomes sig…
Tomasz J. Kozubowski, Andrey Sarantsev, James A. Spiker
arXiv · arXiv q-fin · 2025
We develop a theoretical framework that aims to link micro-level option hedging and stock-specific factor exposure with macro-level market turbulence and explain endogenous volatility amplification during gamma-squeeze events. By explicitly modeling market-maker delta-neutral hedging and incorporating beta-dependent volatility normalization, we derive a stability condition that characterizes the onset of a gamma-sque…
Haoying Dai
arXiv · arXiv q-fin · 2022
In liquid option markets, W-shaped implied volatility curves have occasionally be observed. We show that such shapes can be reproduced in a mixture of two variance-gamma models. This is in contrast to lognormal models, where at least three different distributions have to be mixed in order to produce a W-shape, as recently shown by Glasserman and Pirjol.
Martin Keller-Ressel
arXiv · arXiv q-fin · 2021
Following Boukai (2021) we present the Generalized Gamma (GG) distribution as a possible RND for modeling European options prices under Heston's (1993) stochastic volatility (SV) model. This distribution is seen as especially useful in situations in which the spot's price follows a negatively skewed distribution and hence, Black-Scholes based (i.e. the log-normal distribution) modeling is largely inapt. We apply the …
Ben Boukai
arXiv · arXiv q-fin · 2021
The purpose of this article is to introduce a new Lévy process, termed Variance Gamma++ process, to model the dynamic of assets in illiquid markets. Such a process has the mathematical tractability of the Variance Gamma process and is obtained applying the self-decomposability of the gamma law. Compared to the Variance Gamma model, it has an additional parameter representing the measure of the trading activity. We gi…
M. Gardini, P. Sabino, E. Sasso
arXiv · arXiv q-fin · 2015
This paper introduces the Inverse Gamma (IGa) stochastic volatility model with time-dependent parameters, defined by the volatility dynamics $dV_{t}=κ_{t}\left(θ_{t}-V_{t}\right)dt+λ_{t}V_{t}dB_{t}$. This non-affine model is much more realistic than classical affine models like the Heston stochastic volatility model, even though both are as parsimonious (only four stochastic parameters). Indeed, it provides more real…
Nicolas Langrené, Geoffrey Lee, Zili Zhu
arXiv · arXiv q-fin · 2013
Exact path simulation of the underlying state variable is of great practical importance in simulating prices of financial derivatives or their sensitivities when there are no analytical solutions for their pricing formulas. However, in general, the complex dependence structure inherent in most nontrivial stochastic volatility (SV) models makes exact simulation difficult. In this paper, we present a nontrivial SV mode…
Lancelot F. James, Dohyun Kim, Zhiyuan Zhang
arXiv · arXiv q-fin · 2026
We introduce a structural framework for the geometry of financial order books in which liquidity, supply, and demand are treated as emergent observables rather than primitive market variables. The market is modeled as a relational substrate without assumed metric, temporal, or price coordinates. Observable quantities arise only through observation, implemented here as a reduction of relational degrees of freedom foll…
João P. da Cruz
arXiv · arXiv q-fin · 2026
We propose a structural framework for the geometry of financial order books in which liquidity, supply, and demand are treated as emergent observables rather than primitive economic variables. The market is modeled as an inflationary relational system without assumed metric, temporal, or price coordinates. Observable quantities arise only through projection, implemented here via spectral embeddings of the graph Lapla…
João P. da Cruz
arXiv · arXiv q-fin · 2021
AMMs are autonomous smart contracts deployed on a blockchain that make markets between different assets that live on that chain. In this paper we are examining a specific class of AMMs called Constant Function Market Makers whose trading profile, ignoring fees, is determined by their bonding curve. This class of AMM suffers from what is commonly referred to as Impermanent Loss, which we have previously identified as …
Stefan Loesch, Nate Hindman, Mark B Richardson, Nicholas Welch
arXiv · arXiv q-fin · 2025
For quantitative trading risk management purposes, we present a novel idea: the realized local volatility surface. Concisely, it stands for the conditional expected volatility when sudden market behaviors of the underlying occur. One is able to explore risk management usages by following the orthotical Delta-Gamma dynamic hedging framework. The realized local volatility surface is, mathematically, a generalized Wiene…
Yuming Ma, Shintaro Sengoku, Kazuhide Nakata
arXiv · arXiv q-fin · 2024
In this paper, we present an artificial neural network framework for portfolio compression of a large portfolio of European options with varying maturities (target portfolio) by a significantly smaller portfolio of European options with shorter or same maturity (compressed portfolio), which also represents a self-replicating static hedge portfolio of the target portfolio. For the proposed machine learning architectur…
Vikranth Lokeshwar Dhandapani, Shashi Jain
arXiv · arXiv q-fin · 2024
This research presents a comprehensive evaluation of systematic index option-writing strategies, focusing on S&P500 index options. We compare the performance of hedging strategies using the Black-Scholes-Merton (BSM) model and the Variance-Gamma (VG) model, emphasizing varying moneyness levels and different sizing methods based on delta and the VIX Index. The study employs 1-minute data of S&P500 index options and in…
Maciej Wysocki, Robert Ślepaczuk
arXiv · arXiv q-fin · 2020
The recent development of quantum computing gives us an opportunity to explore its potential applications to many fields, with the field of finance being no exception. In this paper, we apply the deep quantum neural network proposed by Beer et al. (2020) and discuss such potential in the context of simple experiments such as learning implied volatilities and option prices. Furthermore, Greeks such as delta and gamma,…
Takayuki Sakuma
arXiv · arXiv q-fin · 2012
In a stochastic volatility framework, we find a general pricing equation for the class of payoffs depending on the terminal value of a market asset and its final quadratic variation. This allows a pricing tool for European-style claims paying off at maturity a joint function of the underlying and its realised volatility/variance. We study the solution under different stochastic volatility models, give a formula for t…
Lorenzo Torricelli
arXiv · arXiv q-fin · 2009
It is well documented that a model for the underlying asset price process that seeks to capture the behaviour of the market prices of vanilla options needs to exhibit both diffusion and jump features. In this paper we assume that the asset price process $S$ is Markov with cadlag paths and propose a scheme for computing the law of the realized variance of the log returns accrued while the asset was trading in a prespe…
A. Mijatovic, H. Lo
arXiv · arXiv q-fin · 2008
This paper presents hedging strategies for European and exotic options in a Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con- structed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European options, static hedging is implemented. It is shown that perfect hedging can be achieved. Delta and gamma…
Wing Yan Yip, Sofia Olhede, David Stephens
arXiv · arXiv · 2026
Financial decision systems require fast surrogate models for pricing, calibration, hedging, XVA, stress testing, and portfolio optimization. Standard neural surrogates reproduce prices or risk quantities, but downstream tasks depend as much on derivatives: deltas, vegas, curve and credit-spread sensitivities, exposure and objective gradients. We formulate a derivative-informed operator-learning framework in which the…
Miquel Noguer I Alonso