Probability Distribution Of Price Research Articles

A path integral based model for stocks and order dynamics

We present a model for the short-term dynamics of financial assets based on an application to finance of quantum gauge theory, developing ideas of Ilinski. We present a numerical algorithm for the computation of the probability distribution of prices and compare the results with APPLE stocks prices and the S&P500 index.

Strengthening Banks' Portfolio Against Asset Shocks: A Genetic Computational Approach

This thesis investigates models of market risk assessment based on genetic algorithms, with specific reference to asset portfolio choice under volatile market conditions. It does so by developing computational simulations of asset portfolios, which are then subjected to stressful price events. A genetic algorithm functions as an optimising process, allowing portfolios to evolve towards a structure that is – on average – less fragile against asset shocks. The importance of this research is dictated by the grave outcomes of, for instance, the 2008 financial crisis: 371 commercial banks failed between 1/1/2008 and 1/7/2011 in the United States alone. Such events highlighted the need for the renovation of the financial risk framework supposed to at least partially shield banks from unexpected adverse events.A synthetic, computational model is constructed, where asset portfolios are structured so as to invest in four main asset categories: sovereign bonds, financial institutions bonds, corporate bonds and real estate. Each of the categories has an underlying non-normal probability distribution of prices, empirically derived by the literature. These are used to simulate volatile and adverse scenarios affecting the value of the portfolios. A genetic algorithm is designed to select, crossover and mutate, at each generation, the portfolios that best perform under the simulated conditions. After a number of generations, it is expected that one or more portfolios structures will be highlighted as the ones that best perform under adverse scenarios.The model is run three times with different sets of optimization constraints, each specifying the minimum relative proportion of portfolios to be dedicated to each asset category. All versions of the model indicate that the best performing portfolios structures under volatile conditions are the ones that are mainly composed by the asset category featuring less fat tails. The results of the model are checked for their robustness, by running versions with different sets of simulated scenarios and additional numbers of synthetic asset categories. Limitations of the design of the study are identified. The model lacks a simulation of the liability side of financial institutions, and its results are not tested on a systemic level, thus not shedding light on what consequences the indicated portfolio strategy for a single bank would have on the network of banks. Such issues will be addressed in future research.

Intelligent Simulation Method and its Application on Risk Analysis

This article describes an intelligent simulation method for measuring price risk, which is still one of the important problems for various risk managements and need to be studied profoundly. To solve this problem, risk measured in terms of Value at Risk on electricity price is proposed by intelligent simulation. In this work, prices under various market scenarios are produced by intelligent model using fuzzy neural network (FNN). After that, the quantitative model for price risk analysis is built in the form of a function of the estimated probability distribution of price, where price VAR is determined from the distribution according to parameter set, i.e. confidence level. The proposed method is more realistic and effective than variance approach to provide the assessment of the potential loss of electricity price over some period of time.

Generation self-scheduling with partial information on the probability distribution of prices

Recent research has shown that generation self-scheduling in electricity markets can be approached using conditional value-at-risk (CVaR). This study considers a worst-case CVaR methodology applicable to cases where only partial information on the underlying probability distribution of prices is given. In particular, the probability distribution is considered under box and ellipsoidal uncertainty structures. It is shown that both structures result in self-scheduling problems that can be formulated as a quadratic cone program. The cone program can be used to (i) compute the worst-case conditional robust profit with probability level β and (ii) optimise the self-schedule for a pre-specified probability β of the corresponding worst-case conditional robust profit. Simulation results are used to demonstrate the self-scheduling model based on the worst-case CVaR. The usefulness of the proposed model is established by contrasting it with the CVaR approach.

An Optimal Approximate Dynamic Programming Algorithm for the Lagged Asset Acquisition Problem

We consider a multistage asset acquisition problem where assets are purchased now, at a price that varies randomly over time, to be used to satisfy a random demand at a particular point in time in the future. We provide a rare proof of convergence for an approximate dynamic programming algorithm using pure exploitation, where the states we visit depend on the decisions produced by solving the approximate problem. The resulting algorithm does not require knowing the probability distribution of prices or demands, nor does it require any assumptions about its functional form. The algorithm and its proof rely on the fact that the true value function is a family of piecewise linear concave functions.

Worst-Case Robust Profit in Generation Self-Scheduling

Recent research has shown that portfolio optimization theory can be extended to generation self-scheduling in a competitive energy market. This letter considers the self-scheduling problem in the case where the mean vector and covariance matrix of the probability distribution of prices are only known within given bounds, and the probability distribution is otherwise arbitrary. Under the above assumptions, it is shown that a method for optimization over symmetric cones can be used to (1) compute the worst-case robust profit with probability level beta and (2) optimize the self-schedule for a given probability level beta of the corresponding worst-case robust profit.

Study on probability distribution of prices in electricity market: A case study of zhejiang province, china

The study on probability density function and distribution function of electricity prices contributes to the power suppliers and purchasers to estimate their own management accurately, and helps the regulator monitor the periods deviating from normal distribution. Based on the assumption of normal distribution load and non-linear characteristic of the aggregate supply curve, this paper has derived the distribution of electricity prices as the function of random variable of load. The conclusion has been validated with the electricity price data of Zhejiang market. The results show that electricity prices obey normal distribution approximately only when supply-demand relationship is loose, whereas the prices deviate from normal distribution and present strong right-skewness characteristic. Finally, the real electricity markets also display the narrow-peak characteristic when undersupply occurs.

Phase transition of dynamical herd behaviors for Yen–Dollar exchange rates

We study the herd behavior and the phase transition for the yen–dollar exchange rate in the Japanese financial market. It is obtained that the probability distribution of returns satisfies the power-law behavior P ( R ) ≃ R - β with scaling exponents β = 3.11 , 2.81, and 2.29 at time intervals τ = 1 min , 30 min , and 1 h. The crash region in which the probability density increases with the increasing return appears, when the herding parameter h satisfies h ⩾ 2.33 for the case of τ < 30 min . We especially obtain that no crash occurs τ > 30 min and that the probability distribution of price returns occurs in the phase transition at τ = 30 min .

Multifractal Measures for Bond Futures Prices in Futures Exchange Market

We study the tick dynamical behavior of the bond futures price using the rescaled range analysis (R/S analysis) in Korean futures exchange market. For our case, the multifractal Hurst exponents with long-run memory effects can be obtained from two kinds of Korean treasury bond futures transacted recently. It exists no crossover for the Hurst exponents at charateristic time scales. Particularly, we find that our result for probability distribution of prices is similar to a Lorentz distribution different from fat-tailed properties of bond futures price.

Price dynamics in the Bangladesh rice market: implications for public intervention

AbstractIn this paper, the price dynamics of a rice market are examined using dynamic programming techniques. The model is parameterised to the case of Bangladesh and thus represents the situation of a very poor country which has characteristically high price elasticity (due to income effects) and high storage and interest costs. The incentives for private sector storage and its impact on price stability are examined. Various options for public intervention in the storage sector are also explored, including price ceiling schemes and subsidisation of storage costs. Results show that interventions that remove private disincentives (such as storage subsidies) are much cheaper than direct intervention by government, but the impact on the probability distribution of prices is quite different. The effect of trade on the probability distribution of prices is also examined.

Price dynamics in the Bangladesh rice market: implications for public intervention

In this paper, the price dynamics of a rice market are examined using dynamic programming techniques. The model is parameterised to the case of Bangladesh and thus represents the situation of a very poor country which has characteristically high price elasticity (due to income effects) and high storage and interest costs. The incentives for private sector storage and its impact on price stability are examined. Various options for public intervention in the storage sector are also explored, including price ceiling schemes and subsidisation of storage costs. Results show that interventions that remove private disincentives (such as storage subsidies) are much cheaper than direct intervention by government, but the impact on the probability distribution of prices is quite different. The effect of trade on the probability distribution of prices is also examined.

Is risk-sharing resource taxation in society's best interests if prices are log-normally distributed?

This paper contributes to our understanding of the perceived benefits for society of risk-sharing resource taxation. In the particular context of log-normally distributed prices a model is developed which enables comparison of risk-sharing resource taxation with an alternative in determining the overall return to society from auctioning an extraction lease. The main finding of the paper is a potential exception to the general preference for risk-sharing resource taxation if the bidding firms are effectively risk neutral. This exception is illustrated numerically in the context of the impact of increased price uncertainty, but it is shown not to be robust with respect to divergences from risk neutrality in the risk attitudes of firms. Consequently, it is concluded that the choice of risk-sharing resource taxation is likely to be in society's best interests, regardless of the probability distribution of prices.

Economic Harvesting of Uneven-Aged Northern Hardwood Stands Under Risk: A Markovian Decision Model

Abstract A method is presented to determine economic harvesting policies for northern hardwood stands, taking into account uncertain stand growth and prices. The method used a transition matrix giving the probability of a stand and market state in five years, given the current stand and market state. Stand states were defined by the basal area of trees in three timber sizes. Market states were defined by timber price levels. The transition probabilities were computed by simulation, using a stochastic model of northern hardwoods and the probability distribution of prices in Wisconsin. A method of successive approximations was used to find the harvesting policy that would maximize the expected net discounted value of returns from a stand over an infinite horizon. The solution also gave the expected stand value, including land. The best management policy prescribed a specific harvest for each possible stand and market state. A sensitivity analysis was done of the effects of changes in discount rate, fixed costs, and transition probabilities on the best policy and the expected cutting cycle. For. Sci. 33(4):889-907.

Price-making in a competitive market

An attempt is made to analyze the behavior of a price-maker in a purely competitive market. Assuming the price-maker maximizes expected profit subject to the constraint of satisfying periodic excess demand, we derive characteristics of his optimal prices as they depend on current state variables and then obtain properties of the expectation and variance of the long-run stationary probability distribution of price.