arXiv · arXiv q-fin · 2026
In this paper, we present a numerical method for option pricing and the computation of Greeks under stochastic volatility Bachelier-type models, based on elementary linear algebra. The method allows option prices and Greeks to be computed for infinitely many strikes (within a range of convergence) by evaluating only a finite number of expectations, independent of the number of strikes. For the SABR model, we derive a…
Elisa Alòs, Òscar Burés
arXiv · arXiv q-fin · 2020
In the framework of technical analysis for algorithmic trading we use a linear algebra approach in order to define classical technical indicators as bounded operators of the space $l^\infty(\mathbb{N})$. This more abstract view enables us to define in a very simple way the no-lag versions of these tools. Then we apply our results to a basic trading system in order to compare the classical Elder's impulse system with …
Frédéric Butin
arXiv · arXiv q-fin · 2018
The paper proposes an expanded version of the Local Variance Gamma model of Carr and Nadtochiy by adding drift to the governing underlying process. Still in this new model it is possible to derive an ordinary differential equation for the option price which plays a role of Dupire's equation for the standard local volatility model. It is shown how calibration of multiple smiles (the whole local volatility surface) can…
Peter Carr, Andrey Itkin
arXiv · arXiv q-fin · 2017
This paper presents a discrete-time option pricing model that is rooted in Reinforcement Learning (RL), and more specifically in the famous Q-Learning method of RL. We construct a risk-adjusted Markov Decision Process for a discrete-time version of the classical Black-Scholes-Merton (BSM) model, where the option price is an optimal Q-function, while the optimal hedge is a second argument of this optimal Q-function, s…
Igor Halperin
arXiv · arXiv q-fin · 2016
We present a non-parametric method to estimate the discount curve from market quotes based on the Moore-Penrose pseudoinverse. The discount curve reproduces the market quotes perfectly, has maximal smoothness, and is given in closed-form. The method is easy to implement and requires only basic linear algebra operations. We provide a full theoretical framework as well as several practical applications.
Damir Filipović, Sander Willems
arXiv · arXiv q-fin · 2012
The SABR model is a stochastic volatility model not admitting a closed form solution. Hagan, Kumar, Leniewski and Woodward have obtained an approximate solution by means of perturbative techniques. A more precise approximation was found by Henry-Labordère with the heat kernel expansion method. The latter relies on deep and hard theorems from Riemannian geometry which are almost totally unknown to the professionals of…
Carmelo Vaccaro
arXiv · arXiv q-fin · 2010
The goal of this article is to understand some interesting features of sequences of arbitrage operations, which look relevant to various processes in Economics and Finances. In the second part of the paper, analysis of sequences of arbitrages is reformulated in the linear algebra terms. This admits an elegant geometric interpretation of the problems under consideration linked to the asynchronous systems theory. We fe…
Victor Kozyakin, Brian O'Callaghan, Alexei Pokrovskii
arXiv · arXiv q-fin · 2009
Constant Proportion Portfolio Insurance (CPPI) is a strategy designed to give participation in a risky asset while protecting the invested capital. Some gap risk due to extreme events is often kept by the issuer of the product: a put option on the CPPI strategy is included in the product. In this paper we present a new method for the pricing of CPPIs and options on CPPIs, which is much faster and more accurate than t…
Louis Paulot, Xavier Lacroze
arXiv · arXiv · 2026
Market efficiency relies fundamentally on stable liquidity. Consequently, forecasting liquidity dynamics is a priority for both investors and regulators. We introduce a new tail-risk metric, Illiquidity-at-Risk (IlliQaR), designed to quantify the magnitude of extreme liquidity dry-ups. Relying upon the realized Amihud (a precise illiquidity measurement derived from high-frequency data as the ratio of realized volatil…
Demetrio Lacava, Paolo Santucci de Magistris
arXiv · arXiv · 2026
We develop a continuous-time structural dynamic model to determine the exact insolvency regions of banks arising from the non-linear interaction between liquidity and credit risk. While existing literature predominantly treats these risks in isolation or via reduced-form specifications, we explicitly model the feedback loop where funding shocks and regulatory constraints force balance-sheet adjustments that can lead …
Nader Karimi, Davood Ahmadian
arXiv · arXiv · 2026
We develop a variational formulation of Kyle's model of informed trading that accommodates stochastic liquidity and multiple traded assets. The main equilibrium result is stated first: under a martingale dual condition, a matrix-valued martingale depth process generates a linear-Gaussian equilibrium with stochastic matrix-valued price impact. We derive this martingale from a primal-dual problem, inspired by causal op…
Ibrahim Ekren, Evangelos A. Nikitopoulos, Lu Vy
arXiv · arXiv · 2026
Building event-conditioned market models requires separating macro-event labels from persistent microstructure state. We study this distinction in Binance BTCUSDT and ETHUSDT futures from 2023-2026, combining top-20 L2 order book data, trade-flow records, and macro-event windows. We define a supervised discrete L2 liquidity-state transition task, distinct from latent-regime detection and price-direction prediction, a…
Joohyoung Jeon
arXiv · arXiv · 2026
We examine how heavy-tailed liquidity demand changes price discovery in a sequential limit order book with asymmetric information. In our setting, liquidity suppliers observe aggregate order flow, not its decomposition into informed demand and uninformed liquidity shocks. With heavy-tailed uninformed aggregated order flow, large trades remain plausibly uninformed over a wider range of depths, flattening price impact …
Umut Çetin, Mingwei Lin, Giulia Livieri
arXiv · arXiv · 2026
We show that net demand for liquidity by algo strategies is identifiable from its trade and price history alone, with no knowledge of its signal or optimization problem. An exact multi-period regret decomposition implies that the sign of this statistic classifies a linear strategy as a net liquidity consumer or provider, recovering the Kyle (1985) informed-trader/market-maker dichotomy from observables alone. Under a…
Irene Aldridge
arXiv · arXiv · 2026
Hit ratio is a common service metric for electronic corporate bond market making, but raw hit-ratio targets can be economically misleading when client flow has heterogeneous adverse-selection content. This paper extends a stochastic-control framework for OTC bond RFQ market making with hit-ratio constraints by replacing raw hit ratio with a residual-quality-adjusted hit ratio. The key modelling distinction is that ad…
Bouna Niang
arXiv · arXiv · 2026
This paper develops a robust mathematical framework for Constant Function Market Makers (CFMMs) by transitioning from traditional token reserve analyses to a coordinate system defined by price and intrinsic liquidity. We establish a canonical parametrization of the bonding curve that ensures dimensional consistency across diverse trading functions, such as those employed by Uniswap and Balancer, and demonstrate that …
Jimmy Risk, Shen-Ning Tung, Tai-Ho Wang
arXiv · arXiv · 2026
Three traits of decentralized finance are studied. First, the market impact function is derived for optimal-growth liquidity providers. For a standard random walk, the classic square-root impact is recovered. An extension is then derived to fit general fractional Ornstein-Uhlenbeck processes. These findings break with the linearized liquidity models used in most decentralized exchanges. Second, a Constant Product Mar…
B. K. Meister
arXiv · arXiv · 2025
We introduce the Consensus-Bottleneck Asset Pricing Model (CB-APM), which embeds aggregate analyst consensus as a structural bottleneck, treating professional beliefs as a sufficient statistic for the market's high-dimensional information set. Unlike post-hoc explainability approaches, CB-APM achieves interpretability-by-design: the bottleneck constraint functions as an endogenous regularizer that simultaneously impr…
Changeun Kim, Younwoo Jeong, Bong-Gyu Jang