Related papers: A simplified Capital Asset Pricing Model
The market weight of a stock is its capitalization (cap) divided by the total market cap. Rank these weights from top to bottom. The capital distribution curve is a plot of weights versus ranks. For the US stock market, it is linear on a…
An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and…
This paper studies the concept of instantaneous arbitrage in continuous time and its relation to the instantaneous CAPM. Absence of instantaneous arbitrage is equivalent to the existence of a trading strategy which satisfies the CAPM beta…
We introduce a new system of stochastic differential equations which models dependence of market beta and unsystematic risk upon size, measured by market capitalization. We fit our model using size deciles data from Kenneth French's data…
The space of call price functions has a natural noncommutative semigroup structure with an involution. A basic example is the Black--Scholes call price surface, from which an interesting inequality for Black--Scholes implied volatility is…
Modeling the behavior of stock price data has always been one of the challengeous applications of Artificial Intelligence (AI) and Machine Learning (ML) due to its high complexity and dependence on various conditions. Recent studies show…
Based on the analog between the stochastic dynamics and quantum harmonic oscillator, we propose a market force driving model to generalize the Black-Scholes model in finance market. We give new schemes of option pricing, in which we can…
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…
In this paper we provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market originally proposed in [1]. The model takes the form of an interacting generalization of the geometric Brownian…
This paper highlights the hidden dependence of the basic pricing equation of a multi-period consumption-based asset pricing model on price and payoff autocorrelations. We obtain the approximations of the basic pricing equation that describe…
The mathematical model of a linear system with the short memory about own stochastic behavior is proposed. It is assumed that the system is under a continual influence of independent stochastic impulses. In a short memory approximation the…
A derivative is a financial security whose value is a function of underlying traded assets and market outcomes. Pricing a financial derivative involves setting up a market model, finding a martingale (``fair game") probability measure for…
With the development of artificial intelligence technology, quantitative trading systems represented by reinforcement learning have emerged in the stock trading market. The authors combined the deep Q network in reinforcement learning with…
This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes.…
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.
As a typical representation of complex networks studied relatively thoroughly, financial market presents some special details, such as its nonconservation and opinions spreading. In this model, agents congregate to form some clusters, which…
In decentralized finance, any individual can pool their assets into an automated market maker (AMM) -- herein we focus on the constant product market maker (CPMM) -- in exchange for a claim on a fraction of future pool assets and fees…
We derive a closed-form solution for the price of an average price as well as an average strike geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also…
This paper deals with an extension of the so-called Black-Scholes model in which the volatility is modeled by a linear combination of the components of the solution of a differential equation driven by a fractional Brownian motion of Hurst…
As markets have digitized, the number of tradable products has skyrocketed. Algorithmically constructed portfolios of these assets now dominate public and private markets, resulting in a combinatorial explosion of tradable assets. In this…