A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper challenges the notion that asset return doesn't affect Black-Scholes-Merton model.
Modeling stochastic arbitrage bubbles in Black-Scholes framework.
Derives Black-Scholes model without stochastic calculus or PDEs.
Generalizes Black-Scholes model for option pricing under uncertainty.
Study reviews Bachelier model for negative oil prices post-COVID.
Paper revisits Black-Scholes model, proving solution existence and measuring market uncertainty.
Enhanced Black-Scholes model for option pricing with stochastic volatility and interest rate variability.
Black-Scholes equation, after a certain coordinate transformation, is equivalent to the heat equation. On the other hand the relativistic extension of the latter, the telegraphers equation, can be derived from the Euclidean version of the Dirac equation. Therefore the relativistic extension of the Black-Scholes model f…
Quantum mechanics models for financial Black-Scholes model.
The Black-Scholes model (sometimes known as the Black-Scholes-Merton model) gives a theoretical estimate for the price of European options. The price evolution under this model is described by the Black-Scholes formula, one of the most well-known formulas in mathematical finance. For their discovery, Merton and Scholes…
Efficient numerical method for time-fractional Black-Scholes model.
Motivated by the work of Segal and Segal on the Black-Scholes pricing formula in the quantum context, we study a quantum extension of the Black-Scholes equation within the context of Hudson-Parthasarathy quantum stochastic calculus. Our model includes stock markets described by quantum Brownian motion and Poisson proce…
This paper analyzes the probability flow in the stock market using the Black-Scholes model.
An investor faced with a contingent claim may eliminate risk by perfect hedging, but as it is often quite expensive, he seeks partial hedging (quantile hedging or efficient hedging) that requires less capital and reduces the risk. Efficient hedging for European call option was considered in the standard Black-Scholes m…
We apply Gauge Theory of Arbitrage (GTA) {hep-th/9710148} to derivative pricing. We show how the standard results of Black-Scholes analysis appear from GTA and derive correction to the Black-Scholes equation due to a virtual arbitrage and speculators reaction on it. The model accounts for both violation of the no-arbit…
This paper compares analytical and numerical solutions of the Black-Scholes model.
Random neural nets learn Black-Scholes PDEs without dimensionality issues.
Enhancing the Black-Scholes model with Lévy processes and Malliavin calculus
We study the risk premium impact in the Perturbative Black Scholes model. The Perturbative Black Scholes model, developed by Scotti, is a subjective volatility model based on the classical Black Scholes one, where the volatility used by the trader is an estimation of the market one and contains measurement errors. In t…
This paper analyzes hedge errors in Black-Scholes models using finite difference techniques.
Modified perturbation method removes non-smoothness in solving Black-Scholes equations.
Deep learning outperforms Black-Scholes in Brazilian Petrobras option pricing.
Unified model integrates Bachelier and Black-Scholes-Merton for asset pricing.
In this paper we consider a new mathematical extension of the Black-Scholes model in which the stochastic time and stock share price evolution is described by two independent random processes. The parent process is Brownian, and the directing process is inverse to the totally skewed, strictly α-stable process. The subo…
This research improves option pricing models using Heston, GARCH, and jump diffusion models.
Study finds a small correction to Asian option volatility.
Paper solves bond option pricing with credit risk using Black-Scholes equations.
A machine learning approach to compute Black-Scholes prices with uncertain volatility.
Proposes a new model to price options considering market forces beyond Black-Scholes.
Neural network learns to solve Black-Scholes for stock options.
Analytical approximations for Asian option sensitivities in Black-Scholes model.
Improved bounds for Black-Scholes volatility lead to faster root-finding.
In the present work, we propose a new multifactor stochastic volatility model in which slow factor of volatility is approximated by a parabolic arc. We retain ourselves to the perturbation technique to obtain approximate expression for European option prices. We introduce the notion of modified Black-Scholes price. We …
The paper proposes a different method of solving a simplified version of the Black-Scholes equation. This paper will discuss the importance of the Black-Scholes equation and its applications in finance.
We consider conditional-mean hedging in a fractional Black-Scholes pricing model in the presence of proportional transaction costs. We develop an explicit formula for the conditional-mean hedging portfolio in terms of the recently discovered explicit conditional law of the fractional Brownian motion.
We analyze a generalized version of the Black-Scholes equation depending on a parameter . It satisfies the martingale condition and coincides with the Black-Scholes equation in the limit case . We show that the generalized equation is exactly solvable in terms of Hermite polynomials a…
Study approximates financial market with discrete-time models.
Machine learning models outperform traditional option pricing models.
An interacting Black-Scholes model for option pricing, where the usual constant interest rate r is replaced by a stochastic time dependent rate r(t) of the form r(t)=r+f(t) dW/dt, accounting for market imperfections and prices non-alignment, was developed in [1]. The white noise amplitude f(t), called arbitrage bubble,…
Using Maple, we compute some analytical solutions of a modified Black-Scholes equation, recently proposed, in the case of the European put option. We show that the modified Black-Scholes equation with the European put option is exactly solvable in terms of associated Laguerre polynomials. We make some numerical experim…
Trains neural nets for gamma hedging with model uncertainty.
Market illiquidity, feedback effects, presence of transaction costs, risk from unprotected portfolio and other nonlinear effects in PDE based option pricing models can be described by solutions to the generalized Black-Scholes parabolic equation with a diffusion term nonlinearly depending on the option price itself. Di…
We show that the non Hermitian Black-Scholes Hamiltonian and its various generalizations are eta-pseudo Hermitian. The metric operator eta is explicitly constructed for this class of Hamitonians. It is also shown that the effective Black-Scholes Hamiltonian and its partner form a pseudo supersymmetric system.
The paper solves a complex option pricing model using finite elements.
Paper applies subdiffusive dynamics to American and barrier options pricing.
The purpose of this survey chapter is to present a transformation technique that can be used in analysis and numerical computation of the early exercise boundary for an American style of vanilla options that can be modelled by class of generalized Black-Scholes equations. We analyze qualitatively and quantitatively the…
We consider option hedging in a model where the underlying follows an exponential Lévy process. We derive approximations to the variance-optimal and to some suboptimal strategies as well as to their mean squared hedging errors. The results are obtained by considering the Lévy model as a perturbation of the Black-Schole…
Enhances option pricing with fractional order Black-Scholes-Merton model.