scholarly journals Exact and Asymptotic Solutions of the Call Auction Problem

2015 ◽  
Vol 01 (01) ◽  
pp. 1550001 ◽  
Author(s):  
Ioane Muni Toke
Keyword(s):  
Financial Markets ◽  
General Distribution ◽  
Asymptotically Normal ◽  
Price Range ◽  
Weak Limits ◽  
Call Auction ◽  
Trading Mechanism ◽  
Random Indices ◽  
Opening And Closing ◽  
Analytical Expressions

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 F, and may be cancelled at any time. We compute the analytical expressions of the distributions of the traded volume, of the lower and upper bounds of the clearing prices, and of the price range of these possible clearing prices of the call auction. Using results from the theory of order statistics and a theorem on the limit of sequences of random variables with independent random indices, we derive the weak limits of all these distributions. In this setting, traded volume and bounds of the clearing prices are found to be asymptotically normal, while the clearing price range is asymptotically exponential. All the parameters of these distributions are explicitly derived as functions of the parameters of the incoming orders' flows.

Strip yield model for multiple straight cracks with coalesced yield zones: A theoretical study

2021 ◽  
pp. 1-15
Author(s):  
S. Hasan ◽  
N. Akhtar ◽  
S. Shekhar
Keyword(s):  
Numerical Study ◽  
Multiple Cracks ◽  
Principle Of Superposition ◽  
Yield Model ◽  
Zone Length ◽  
Yield Zone ◽  
Strip Yield Model ◽  
Opening And Closing ◽  
The Impact ◽  
Analytical Expressions

The paper presents a complicated case of coalescence of yield zones between two internal cracks out of four collinear straight cracks weakened an infinite isotropic plate. Two solutions are presented for the case of opening and closing of multiple cracks under general yielding conditions. Using these two solutions and the principle of superposition, we found the analytical expressions for load-bearing capacity of the plate using complex variable method. A numerical study has been carried out to investigate the behavior of yield zone length concerning remotely applied stresses at the boundary of the plate and the impact of two outer cracks on the propagation of inner cracks due to coalesced yield zones. Results obtained are reported graphically.

scholarly journals Durfee Polynomials

10.37236/1370 ◽  
1998 ◽  
Vol 5 (1) ◽  
Author(s):  
E. Rodney Canfield ◽  
Sylvie Corteel ◽  
Carla D. Savage
Keyword(s):  
Asymptotic Formula ◽  
Experimental Evidence ◽  
Upper Bound ◽  
Asymptotic Form ◽  
Asymptotically Normal ◽  
The Family ◽  
Average Size ◽  
Durfee Square ◽  
Analytical Expressions ◽  
Addition Formulas

Let ${\bf F}(n)$ be a family of partitions of $n$ and let ${\bf F}(n,d)$ denote the set of partitions in ${\bf F}(n)$ with Durfee square of size $d$. We define the Durfee polynomial of ${\bf F}(n)$ to be the polynomial $P_{{\bf F},n}= \sum |{\bf F}(n,d)|y^d$, where $ 0 \leq d \leq \lfloor \sqrt{n} \rfloor.$ The work in this paper is motivated by empirical evidence which suggests that for several families ${\bf F}$, all roots of the Durfee polynomial are real. Such a result would imply that the corresponding sequence of coefficients $\{|{\bf F}(n,d)|\}$ is log-concave and unimodal and that, over all partitions in ${\bf F}(n)$ for fixed $n$, the average size of the Durfee square, $a_{{\bf F}}(n)$, and the most likely size of the Durfee square, $m_{{\bf F}}(n)$, differ by less than 1. In this paper, we prove results in support of the conjecture that for the family of ordinary partitions, ${\bf P}(n)$, the Durfee polynomial has all roots real. Specifically, we find an asymptotic formula for $|{\bf P}(n,d)|$, deriving in the process a simple upper bound on the number of partitions of $n$ with at most $k$ parts which generalizes the upper bound of Erdös for $|{\bf P}(n)|$. We show that as $n$ tends to infinity, the sequence $\{|{\bf P}(n,d)|\},\ 1 \leq d \leq \sqrt{n},$ is asymptotically normal, unimodal, and log concave; in addition, formulas are found for $a_{{\bf P}}(n)$ and $m_{{\bf P}}(n)$ which differ asymptotically by at most 1. Experimental evidence also suggests that for several families ${\bf F}(n)$ which satisfy a recurrence of a certain form, $m_{{\bf F}}(n)$ grows as $c \sqrt{n}$, for an appropriate constant $c=c_{{\bf F}}$. We prove this under an assumption about the asymptotic form of $|{\bf F}(n,d)|$ and show how to produce, from recurrences for the $|{\bf F}(n,d)|$, analytical expressions for the constants $c_{{\bf F}}$ which agree numerically with the observed values.

scholarly journals THE CLASS OF NONLINEAR STOCHASTIC MODELS AS A BACKGROUND FOR THE BURSTY BEHAVIOR IN FINANCIAL MARKETS

2012 ◽  
Vol 15 (supp01) ◽  
pp. 1250071 ◽  
Author(s):  
VYGINTAS GONTIS ◽  
ALEKSEJUS KONONOVICIUS ◽  
STEFAN REIMANN
Keyword(s):  
Financial Markets ◽  
Stochastic Models ◽  
Numerical Evaluation ◽  
First Passage Time ◽  
Passage Time ◽  
Bessel Process ◽  
Proposed Model ◽  
Nonlinear Stochastic Model ◽  
Bursty Behavior ◽  
Analytical Expressions

We investigate behavior of the continuous stochastic signals above some threshold, bursts, when the exponent of multiplicativity is higher than one. Earlier we have proposed a general nonlinear stochastic model applicable for the modeling of absolute return and trading activity in financial markets which can be transformed into Bessel process with known first hitting (first passage) time statistics. Using these results we derive PDF of burst duration for the proposed model. We confirm derived analytical expressions by numerical evaluation and discuss bursty behavior of return in financial markets in the framework of modeling by nonlinear SDE.

scholarly journals Reference Prices and Turnover: Evidence from Small-Capitalization Stocks

2021 ◽  
Vol 14 (1) ◽  
pp. 29
Author(s):  
Ashish Pandey
Keyword(s):  
Financial Markets ◽  
Reference Price ◽  
Purchase Intention ◽  
Firm Level ◽  
Reference Prices ◽  
Product Pricing ◽  
Price Range ◽  
Portfolio Managers ◽  
Stock Market Investors

A large amount of literature in the field of social psychology and product pricing discusses the role of reference prices in affecting buyer’s price perception and purchase intention. Reference price denotes a standard against which the consumer compares the offer price of a product. In this paper, we investigate whether reference prices play any role in affecting the trading decision of stock market investors. We use firm-level, fixed-effect panel data methodology to empirically investigate whether investors respond to a violation of their internalized reference price range by executing a trading decision. Our results, based on a sample of Indian firms with small capitalization, show that investors respond to a violation of their internalized reference price range by executing a trading decision. However, consistent with the prior findings that investors suffer from myopic loss aversion, they continue to hold the positions when the reference price range is violated on the downside but sell stocks that have violated the high point of the reference price range. Our findings are robust for the reference price ranges that are constructed using the prior day’s trading prices, prior week’s trading prices, and prior year’s trading prices. The portfolio managers can develop a better understanding of expected trading intensity by incorporating reference price range in their models. The policymakers can use our results to find ways to improve the liquidity and efficiency of financial markets.

Is a Stock Exchange a Computer Solution?

2011 ◽  
Vol 3 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Fabian Muniesa
Keyword(s):  
Financial Markets ◽  
North American ◽  
Stock Exchange ◽  
Single Point ◽  
Price Formation ◽  
Computer Solution ◽  
Call Auction ◽  
Definition Of

The paper examines, through a case study on the Arizona Stock Exchange, how computerization challenged the definition of the stock exchange in the context of North-American financial markets in the 1990’s. It analyses exchange automation in terms of trials of explicitness: the computational formulation of what an exchange is calls for a detailed explication of the (variable, often conflicting and unanticipated) processes and properties of price formation. The paper focuses in particular on the argument of the concentration of liquidity in one single point, which was central to the development of the Arizona Stock Exchange (an electronic call auction). It then asks what kind of revolution is the ‘explicitness revolution’ in the design of allocation mechanisms.

Closing Call Auction Prices as Settlement Prices for Derivatives Contracts and Price Manipulation

2015 ◽  
Vol 23 (3) ◽  
pp. 439-473
Author(s):  
Sun-Joong Yoon
Keyword(s):  
Financial Markets ◽  
Financial Market ◽  
Economic Gain ◽  
Price Manipulation ◽  
Auction Price ◽  
Closing Price ◽  
Call Auction ◽  
Auction Prices ◽  
Administrative Penalty ◽  
Manipulation Case

Previous literature emphasizes the importance of a closing call auction system because it can not only improve the price discovery effect, but also mitigate the possibility of price manipulation. However, Korea Exchange, which has adopted a closing call auction system, has still suffered from the price manipulation, most cases of which are likely to be related to the derivatives contracts. Based on this environment, this paper investigates why KRX experiences the closing price manipulations so much, even though it adopted the closing call auction system. Generally, a price manipulation occurs when the legal/administrative penalty is less than the expected economic gain or when a specific market structure increases an incentive to manipulate the price. In this paper, we find that the adoption of a closing call auction price as a settlement price for KOSPI derivatives contracts strengthens the incentive for closing price manipulation, which is supported by Kyle (2007). Kyle (2007) shows that if a closing price is used as a settlement price and investors can execute the ‘market-on-expiration orders’ surely, the derivatives with cash settlement are susceptible to the price manipulation such as squeezing or cornering, equally as the derivatives with physical settlement. As such, KRX is the only financial market that satisfies the above conditions. This paper tries to verify this argument by introducing the Hong Kong Exchange case, the Korean ELS-related manipulation case and the Deutsche Bank case. Therefore, we strongly recommend changing the settlement price of KRX derivatives contracts into an average price, which is similar with the well-developed financial markets.

Is a Stock Exchange a Computer Solution?

2013 ◽  
pp. 117-132 ◽  
Author(s):  
Fabian Muniesa
Keyword(s):  
Financial Markets ◽  
North American ◽  
Stock Exchange ◽  
Single Point ◽  
Price Formation ◽  
Computer Solution ◽  
Call Auction ◽  
Definition Of

The paper examines, through a case study on the Arizona Stock Exchange, how computerization challenged the definition of the stock exchange in the context of North-American financial markets in the 1990’s. It analyses exchange automation in terms of trials of explicitness: the computational formulation of what an exchange is calls for a detailed explication of the (variable, often conflicting and unanticipated) processes and properties of price formation. The paper focuses in particular on the argument of the concentration of liquidity in one single point, which was central to the development of the Arizona Stock Exchange (an electronic call auction). It then asks what kind of revolution is the ‘explicitness revolution’ in the design of allocation mechanisms.

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