We propose a model for price formation in financial markets based on clearing of a standard call auction with random orders, and verify its validity for prediction of the daily closing price distribution statistically. The model considers random buy and sell orders, placed following demand- and supply-side valuation di…
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The study examines European option pricing using a generalized tempered stable distribution.
problem Investigating the pricing of European options under a generalized tempered stable distribution.
method Fitting the Generalized Tempered Stable (GTS) distribution to S\&P 500 Index returns, applying the Esscher transform, and using the Extended Black-Scholes and Generalized Black-Scholes formulas.
result The GTS distribution yields consistent European option prices for deep OTM and ITM options, but underprices near-the-money and in-the-money options compared to the Black-Scholes model.
Report presents analysis of empirical distribution of future returns of bitcoin (BTC) from BTUSD inverse option prices. Logistic pdf is chosen as underlying distribution to fit option prices. The result is satisfactory and suggests that these prices can be described with just three or even one parameter. Fitted Logisti…
Distributions of assets returns exhibit a slight skewness. In this note we show that our model of endogenous price formation \cite{Reimann2006} creates an asymmetric return distribution if the price dynamics are a process in which consecutive trading periods are dependent from each other in the sense that opening price…
Adjusted Closing Pricesq-fin.PM
Historical returns depend on historical closing prices and distributions. We describe how to compute adjusted closing prices from closing price/distribution data with an emphasis on spreadsheet implementation. Then the growth of a security from one date to another (1 + total return) is just the ratio of the correspondi…
We consider a financial market model which consists of a financial asset and a large number of interacting agents classified into many types. Different types of agents are heterogeneous in their price expectations. Each agent can change its type based on the current empirical distribution of the types and the equilibri…
ReVol normalizes stock price features to mitigate distribution shifts, improving prediction accuracy.
problem Distribution shifts in stock price data hinder accurate prediction.
method ReVol uses normalization, attention-based estimation, and geometric Brownian motion.
result ReVol achieves an average improvement of more than 0.03 in IC and over 0.7 in SR.
The paper presents an approximate formula for European mortgage options pricing.
problem Pricing European mortgage options with accuracy and efficiency.
method Approximation of the underlying price distribution using lognormal distributions and matching moments.
result The proposed formula provides a good approximation with high accuracy compared to Monte Carlo simulations.
A simple spin system is constructed to simulate dynamics of asset prices and studied numerically. The outcome for the distribution of prices is shown to depend both on the dimension of the system and the introduction of price into the link measure. For dimensions below 2, the associated risk is high and the price distr…
In this paper the Buchen's pricing formulae of (higher order) asset and bond binary options are incorporated into the pricing formula of power binary options and a pricing formula of "the normal distribution standard options" with the maturity payoff related to a power function and the density function of normal distri…
Using available data from the New York stock market (NYSM) we test four different bi-parametric models to fit the correspondent volume-price distributions at each -minute lag: the Gamma distribution, the inverse Gamma distribution, the Weibull distribution and the log-normal distribution. The volume-price data, whi…
A homogeneously saturated equation for the time development of the price of a financial asset is presented and investigated for the pricing of European call options using noise that is distributed as a Student's t-distribution. In the limit that the saturation parameter of the equation equals zero, the standard model o…
The paper presents an evolutionary economic model for the price evolution of stocks. Treating a stock market as a self-organized system governed by a fast purchase process and slow variations of demand and supply the model suggests that the short term price distribution has the form a logistic (Laplace) distribution. T…
We statistically investigate the distribution of share price and the distributions of three common financial indicators using data from approximately 8,000 companies publicly listed worldwide for the period 2004-2013. We find that the distribution of share price follows Zipf's law; that is, it can be approximated by a …
Novel neural network predicts electricity prices with higher moments.
problem Probabilistic forecasting of volatile electricity prices.
method Distributional neural network with a probability layer.
result Significantly outperforms benchmarks in forecasting.
Explicit expressions for European option pricing under a generalized skew normal distributionq-fin.PR
Under a generalized skew normal distribution we consider the problem of European option pricing. Existence of the martingale measure is proved. An explicit expression for a given European option price is presented in terms of the cumulative distribution function of the univariate skew normal and the bivariate standard …
The call auction is a widely used trading mechanism, especially during the opening and closing periods of financial markets. In this paper, we study a standard call auction problem where orders are submitted according to Poisson processes, with random prices distributed according to a general distribution, and may be c…
New method uses DistRL to estimate entire payoff distribution for financial derivatives.
problem Traditional methods focus on expected option value; this tackles risk-aware pricing.
method Reinterprets and proposes a framework using Distributional Reinforcement Learning (DistRL).
result Demonstrates enhanced risk-aware pricing and uncertainty quantification on Asian options.
Modeling price clustering in financial markets using discrete distributions.
problem Price clustering phenomenon in financial markets.
method Discrete price model based on mixture of double Poisson distributions with dynamic volatility and proportions.
result Higher instantaneous volatility weakens price clustering at ultra-high frequencies.
The principle of absence of arbitrage opportunities allows obtaining the distribution of stock price fluctuations by maximizing its information entropy. This leads to a physical description of the underlying dynamics as a random walk characterized by a stochastic diffusion coefficient and constrained to a given value o…
Model predicts stock price changes and forecasts using tokenized data.
problem Challenges in stock price forecasting and prediction due to dynamic data and statistical differences.
method Introduces PCIE model with tokenization to handle both forecasting and prediction.
result PCIE model outperforms state-of-the-art models in forecast and prediction tasks.
We investigate the pricing of cliquet options in a geometric Meixner model. The considered option is of monthly sum cap style while the underlying stock price model is driven by a pure-jump Meixner--Lévy process yielding Meixner distributed log-returns. In this setting, we infer semi-analytic expressions for the clique…
We examine the correlation of the limit price with the order book, when a limit order comes. We analyzed the Rebuild Order Book of Stock Exchange Electronic Trading Service, which is the centralized order book market of London Stock Exchange. As a result, the limit price is broadly distributed around the best price acc…
The study tackles modeling high-frequency financial data using continuous distributions, finding them inadequate.
problem Challenges in modeling high-frequency integer price changes with continuous distributions.
method Proposed a modified maximum likelihood estimation procedure to account for the discreteness of high-frequency price changes.
result Traditional GARCH models are not suitable for high-frequency data due to the discreteness of price changes.
New online method for multivariate probabilistic electricity price forecasting.
problem Multivariate probabilistic forecasting of electricity prices.
method Online multivariate distributional regression with LASSO regularization.
result Robust and interpretable joint prediction intervals for 24-hour electricity prices.
We investigate a statistical-static hedging technique for pricing assets considered as single-step stochastic cash flows. The valuation is based on constructing in a canonical way a European style derivative on a benchmark security such that the physical payoff distribution coincides with the (corrected) physical asset…
Accurate forecasts of electricity spot prices are essential to the daily operational and planning decisions made by power producers and distributors. Typically, point forecasts of these quantities suffice, particularly in the Nord Pool market where the large quantity of hydro power leads to price stability. However, wh…
New method improves probabilistic electricity price predictions.
problem Improving point forecasts to probabilistic distributions for better decision-making.
method Isotonic Distributional Regression combined with other postprocessing methods.
result Isotonic Distributional Regression outperforms other methods in combining probabilistic distributions.
The Generalized Gamma distribution as a useful RND under Heston's stochastic volatility modelq-fin.CP
GG distribution improves option pricing for negatively skewed spot price distributions.
problem Inaccurate Black-Scholes model for negatively skewed spot price distributions.
method Applied Generalized Gamma (GG) distribution as a Risk-Neutral Density (RND) for Heston's SV model.
result GG distribution better matches market option data with negatively skewed spot price distributions.
Study reveals that cryptocurrency price variations follow power-law distributions, influenced by age and market capitalization.
problem Understanding the statistical properties of cryptocurrencies, especially their price variations.
method Comprehensive investigation of over 7000 digital currencies, analyzing their price returns over time.
result Cryptocurrency price returns follow power-law distributions, with age and market capitalization influencing these distributions.
The distribution of the returns for a stock are not well described by a normal probability density function (pdf). Student's t-distributions, which have fat tails, are known to fit the distributions of the returns. We present pricing of European call or put options using a log Student's t-distribution, which we call a …
Zipf's Law Distributions for Korean Stock Pricescond-mat.stat-mech
This paper investigates the rank distribution, cumulative probability, and probability density of price returns for the stocks traded in the KSE and the KOSDAQ market. This research demonstrates that the rank distribution is consistent approximately with the Zipf's law with exponent (KSE) and -1.31 (KOSDAQ),…
Optimizes risk-neutral probabilities for derivative pricing.
problem Deriving bounds on derivative values under multiple risk-neutral scenarios.
method Convex optimization over the set of risk-neutral probability distributions.
result Tractable finite-dimensional optimization problems for pricing.
Regularization and analytic option pricing under -stable distribution of arbitrary asymmetryq-fin.PR
We consider a non-Gaussian option pricing model, into which the underlying log-price is assumed to be driven by an -stable distribution. We remove the a priori divergence of the model by introducing a Mellin regularization for the Lévy propagator. Using distributional and tools, we derive an analytic …
A new pricing strategy learns customer valuations without noise distribution knowledge.
problem Setting optimal prices for products based on customer valuations with unknown noise.
method Developed a novel perturbed linear bandit framework to learn both contextual functions and market noise.
result Proved sub-linear regret bound and demonstrated superior performance on simulations and real data.
Economic Complexity Limits Accuracy of Price Probability Predictions by Gaussian Distributionsq-fin.GN
Price and return predictions are limited by economic complexity, not just volatility.
problem Limited accuracy of price and return probability forecasts by Gaussian distributions.
method Analyzes economic reasons behind limitations in predicting price and return statistical moments.
result Predictions of price and return probabilities by Gaussian distributions are inaccurate due to economic complexity.
Probability Weighting Meets Heavy Tails: An Econometric Framework for Behavioral Asset Pricingq-fin.MF
Econometric framework integrates heavy-tailed distributions with behavioral probability weighting for better asset pricing.
problem Underestimation of Value-at-Risk by traditional models in asset pricing.
method Developed an econometric framework combining heavy-tailed Student's distributions with behavioral probability weighting.
result Student's specifications outperform Gaussian models in 88.4% of cases, reducing underestimation of Value-at-Risk by 16.5 percentage points.
News and price returns from threshold behaviour and vice-versa: exact solution of a simple agent-based market modelphysics.soc-ph
Starting from an exact relationship between news, threshold and price return distributions in the stationary state, I discuss the ability of the Ghoulmie-Cont-Nadal model of traders to produce fat-tailed price returns. Under normal conditions, this model is not able to transform Gaussian news into fat-tailed price retu…
Barrieu, Rouault, and Yor [J. Appl. Probab. 41 (2004)] determined asymptotics for the logarithm of the distribution function of the Hartman-Watson distribution. We determine the asymptotics of the density. This refinement can be applied to the pricing of Asian options in the Black-Scholes model.
We study an option pricing framework that accounts for the price impact of an earnings announcement (EA), and analyze the behavior of the implied volatility surface prior to the event. On the announcement date, we incorporate a random jump to the stock price to represent the shock due to earnings. We consider different…
Paper uses TCN with attention to predict UHF stock price changes.
problem Predicting discrete dynamic distribution of UHF stock price changes.
method Classified price changes, used TCN with attention mechanism.
result TCN and TCN (attention) models outperform GARCH and LSTM models.
Two price regimes identified in limit order books: close and far from quotes.
problem Understanding the distribution and behavior of limit orders in limit order books.
method Analysis of limit order book data in dimensions of price, time, lifetime, and volume.
result Identification of two distinct regimes in the limit order book: close and far from quotes.
The distribution of a time integral of geometric Brownian motion is not well understood. To price an Asian option and to obtain measures of its dependence on the parameters of time, strike price, and underlying market price, it is essential to have the distribution of time integral of geometric Brownian motion and it i…
New pricing theory solves St. Petersburg paradox.
problem St. Petersburg Paradox unresolved for 280 years.
method Proposes new pricing theory with fair pricing rules.
result New pricing theory resolves the paradox.
Optimal pricing strategy for unknown valuation models with noisy feedback.
problem Minimizing regret in dynamic pricing with unknown valuation functions and noisy feedback.
method Proposes a minimax-optimal algorithm using discretization and data partitioning to handle unknown noise distribution and Lipschitz continuity of valuation functions.
result Achieves minimax-optimal regret bound matching the theoretical lower bound up to logarithmic factors.
We introduce a non-parametric method to recover physical probability distributions of asset returns based on their European option prices and some other sparse parametric information. Thus the main problem is similar to the one considered foir instance in the Recovery Theorem by Ross (2015), except that here we conside…
We study the rank distribution, the cumulative probability, and the probability density of returns of stock prices of listed firms traded in four stock markets. We find that the rank distribution and the cumulative probability of stock prices traded in are consistent approximately with the Zipf's law or a power law. It…
We present a framework for describing the evolution of stochastic observables having a non-stationary distribution of values. The framework is applied to empirical volume-prices from assets traded at the New York stock exchange. Using Kullback-Leibler divergence we evaluate the best model out from four biparametric mod…