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.
Paper revisits Black-Scholes model, proving solution existence and measuring market uncertainty.
This paper analyzes the probability flow in the stock market using the Black-Scholes model.
Proposes a new model to price options considering market forces beyond Black-Scholes.
Study approximates financial market with discrete-time models.
This paper analyzes hedge errors in Black-Scholes models using finite difference techniques.
In common finance literature, Black-Scholes partial differential equation of option pricing is usually derived with no-arbitrage principle. Considering an asset market, Merton applied the Hamilton-Jacobi-Bellman techniques of his continuous-time consumption-portfolio problem, deriving general equilibrium relationships …
Enhanced Black-Scholes model for option pricing with stochastic volatility and interest rate variability.
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…
We prove and test an efficient series representation for the European Black-Scholes call, which generalizes and refines previously known approximations, and works in every market configuration.
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…
Modeling stochastic arbitrage bubbles in Black-Scholes framework.
We show that shortfall risks of American options in a sequence of multinomial approximations of the multidimensional Black--Scholes (BS) market converge to the corresponding quantities for similar American options in the multidimensional BS market with path dependent payoffs. In comparison to previous papers we conside…
Neural network learns to solve Black-Scholes for stock options.
In this paper, we establish a link between quantum stochastic processes, and nonlocal diffusions. We demonstrate how the non-commutative Black-Scholes equation of Accardi & Boukas (Luigi Accardi, Andreas Boukas, 'The Quantum Black-Scholes Equation', Jun 2007, available at arXiv:0706.1300v1) can be written in integral f…
Honest traders can outperform insiders in a Black-Scholes market with positive probability.
Enhancing the Black-Scholes model with Lévy processes and Malliavin calculus
New formula identifies and quantifies costs for automated market makers.
A machine learning approach to compute Black-Scholes prices with uncertain volatility.
We apply Geometric Arbitrage Theory to obtain results in Mathematical Finance, which do not need stochastic differential geometry in their formulation. First, for a generic market dynamics given by a multidimensional Itô's process we specify and prove the equivalence between (NFLVR) and expected utility maximization. A…
Machine learning models outperform traditional option pricing models.
We consider fractional Black-Scholes market with proportional transaction costs. When transaction costs are present, one trades periodically i.e. we have the discrete trading with equidistance between trading times. We derive a non trivial hedging error for a class of European options with convex payoff in the…
A nonlinear wave alternative for the standard Black-Scholes option-pricing model is presented. The adaptive-wave model, representing 'controlled Brownian behavior' of financial markets, is formally defined by adaptive nonlinear Schrödinger (NLS) equations, defining the option-pricing wave function in terms of the stock…
This research improves option pricing models using Heston, GARCH, and jump diffusion models.
Options financial instruments designed to protect investors from the stock market randomness. In 1973, Fisher Black, Myron Scholes and Robert Merton proposed a very popular option pricing method using stochastic differential equations within the Ito interpretation. Herein, we derive the Black-Scholes equation for the o…
The paper develops a new class of financial market models. These models are based on generalized telegraph processes: Markov random flows with alternating velocities and jumps occurring when the velocities are switching. While such markets may admit an arbitrage opportunity, the model under consideration is arbitrage-f…
Study on spontaneous symmetry breaking in financial markets using quantum mechanics.
The paper extends option pricing theory for markets with informed traders.
Informer improves option pricing accuracy in volatile markets.
In this paper we study the continuum time dynamics of a stock in a market where agents behavior is modeled by a Minority Game and a Grand Canonical Minority Game. The dynamics derived is a generalized geometric Brownian motion; from the Black & Scholes formula the calibration of both the Minority Game and the Grand Can…
Families of explicit solutions are found to a nonlinear Black-Scholes equation which incorporates the feedback-effect of a large trader in case of market illiquidity. The typical solution of these families will have a payoff which approximates a strangle. These solutions were used to test numerical schemes for solving …
New formula for implied volatility from Black-Scholes model.
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…
Model financial market with fundraiser and stock, derive option prices.
Paper calculates greeks for DeFi LPs and introduces Impermanent Gain.
The problem of hedging and pricing sequences of contingent claims in large financial markets is studied. Connection between asymptotic arbitrage and behavior of the ~-~quantile price is shown. The large Black-Scholes model is carefully examined.
We justify and give error estimates for binomial approximations of game (Israeli) options in the Black--Scholes market with Lipschitz continuous path dependent payoffs which are new also for usual American style options. We show also that rational (optimal) exercise times and hedging self-financing portfolios of binomi…
Derives explicit investment strategy with random endowment.
Study evaluates cryptocurrency option pricing models, finds Kou and Bates models perform best.
We recently showed that the S&P500 stock market index is well described by Tsallis non-extensive statistics and nonlinear Fokker-Planck time evolution. We argued that these results should be applicable to a broad range of markets and exchanges where anomalous diffusion and `heavy' tails of the distribution are present.…
Differential equations can be used to construct predictive models of a diverse set of real-world phenomena like heat transfer, predator-prey interactions, and missile tracking. In our work, we explore one particular application of stochastic differential equations, the Black-Scholes-Merton model, which can be used to p…
Quantum effects improve stock option pricing model.
In this short note, we study an optimization problem of expected implementation shortfall (IS) cost under general shaped market impact functions. In particular, we find that an optimal strategy is a VWAP (volume weighted average price) execution strategy when the market model is a Black-Scholes type with stochastic clo…
Black-Scholes (BS) is the standard mathematical model for option pricing in financial markets. Option prices are calculated using an analytical formula whose main inputs are strike (at which price to exercise) and volatility. The BS framework assumes that volatility remains constant across all strikes, however, in prac…
A new mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock as well as new initial and boundary conditions. Conventional notions of maturity time and strike prices are not used. The Black-Scholes equation is solved…
We study markets with no riskless (safe) asset. We derive the corresponding Black-Scholes-Merton option pricing equations for markets where there are only risky assets which have the following price dynamics: (i) continuous diffusions; (ii) jump-diffusions; (iii) diffusions with stochastic volatilities, and; (iv) geome…
A new method approximates option pricing in stochastic interest rate markets.
Study liquidity impact on spread option pricing.
This paper extends the Black-Scholes-Merton model to more complex market scenarios.