scholarly journals Algebraic Properties of Arbitrage: An Application to Additivity of Discount Functions

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 868
Author(s):  
Salvador Cruz Rambaud
Keyword(s):  
Financial Markets ◽  
Preference Relation ◽  
General Setting ◽  
Linear Topological Space ◽  
Point Of View ◽  
No Arbitrage ◽  
Algebraic Properties ◽  
Algebraic Concepts ◽  
Probabilistic Point ◽  
Absence Of Arbitrage

Background: This paper aims to characterize the absence of arbitrage in the context of the Arbitrage Theory proposed by Kreps (1981) and Clark (2000) which involves a certain number of well-known financial markets. More specifically, the framework of this model is a linear (topological) space X in which a (convex) cone C defines a vector ordering. There exist markets for only some of the contingent claims of X which assign a price p i to the marketed claim m i . The main purpose of this paper is to provide some novel algebraic characterizations of the no arbitrage condition and specifically to derive the decomposability of discount functions with this approach. Methods: Traditionally, this topic has been focused from a topological or probabilistic point of view. However, in this manuscript the treatment of this topic has been by using purely algebraic tools. Results: We have characterized the absence of arbitrage by only using algebraic concepts, properties and structures. Thus, we have divided these characterizations into those concerning the preference relation and those involving the cone. Conclusion: This paper has provided some novel algebraic properties of the absence of arbitrage by assuming the most general setting. The additivity of discount functions has been derived as a particular case of the general theory.

scholarly journals On the Option Pricing by the Binomial Model

2021 ◽  
Author(s):  
Nikos Halidias
Keyword(s):  
Sufficient Conditions ◽  
Fair Value ◽  
Point Of View ◽  
Binomial Model ◽  
No Arbitrage ◽  
Mathematical Arguments ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Probabilistic Point ◽  
Absence Of Arbitrage

In this note we study the binomial model applied to European, American and Bermudan type of derivatives. Our aim is to give the necessary and sufficient conditions under which we can define a fair value via replicating portfolios for any derivative using simple mathematical arguments and without using no arbitrage techniques. Giving suitable definitions we are able to define rigorously the fair value of any derivative without using concepts from probability theory or stochastic analysis therefore is suitable for students or young researchers. It will be clear in our analysis that if $e^{r \delta} \notin [d,u]$ then we can not define a fair value by any means for any derivative while if $d \leq e^{r \delta} \leq u$ we can. Therefore the definition of the fair value of a derivative is not so closely related with the absence of arbitrage. In the usual probabilistic point of view we assume that $d < e^{r \delta} < u$ in order to define the fair value but it is not clear what we can (or we can not) do in the cases where $e^{r \delta} \leq d$ or $e^{r \delta} \geq u$.

scholarly journals The arbitrage In Securities Market Model And Some There Properties

2021 ◽  
Vol 26 (4) ◽  
pp. 542-549
Author(s):  
Adel Murtda Al-awci ◽  
Noori F. Al-Mayahi
Keyword(s):  
Financial Markets ◽  
Linear Topological Space ◽  
Securities Market ◽  
Market Model ◽  
Separation Theorems ◽  
Topological Spaces ◽  
No Arbitrage ◽  
Mathematical Formulas ◽  
Economic Balance ◽  
Necessary And Sufficient

The  applications of functional analysis in economics began worked out since the  by presenting theoretical studies related to the development and balance of financial  markets by building mathematical models with linear topological space , describing and defining the economic balance of the stock market in mathematical formulas and terms , and then using the theorems of  linear topological spaces such as Han's theorems . Banach , separation theorems  , open function theorem ,closed statement theorem and so on to create the necessary and sufficient condition to make the market model achieve viability , achieve no arbitrage , and not recognize No free Lunches                                                                                                                             

Real-Estate Derivatives

2017 ◽  
Author(s):  
Radu S. Tunaru
Keyword(s):  
Real Estate ◽  
Financial Markets ◽  
Investment Banks ◽  
Financial Instruments ◽  
Stress Tests ◽  
Real World Data ◽  
No Arbitrage ◽  
New Frontier ◽  
Property Price ◽  
Comparative Description

This book brings together the latest concepts and models in real-estate derivatives, the new frontier in financial markets. The importance of real-estate derivatives in managing property price risk that has destabilized economies frequently in the last hundred years has been brought into the limelight by Robert Shiller over the last three decades. In spite of his masterful campaign for the introduction of real-estate derivatives, these financial instruments are still in a state of infancy. This book aims to provide a state-of-the-art overview of real-estate derivatives at this moment in time, covering the description of these financial products, their applications, and the most important models proposed in the literature in this area. In order to facilitate a better understanding of the situations when these products can be successfully used, ancillary topics such as real-estate indices, mortgages, securitization, and equity release mortgages are also discussed. The book is designed to pay attention to the econometric aspects of realestate index prices, time series, and also to financial engineering no-arbitrage principles governing pricing of derivatives. The emphasis is on understanding the financial instruments through their mechanics and comparative description. The examples are based on real-world data from exchanges or frommajor investment banks or financial houses in London. The numerical analysis is easily replicable with Excel and Matlab. This is the most advanced published book in this area, combining practical relevance with intellectual rigour. Real-estate derivatives will become important for managing macro risks in order to pass stress tests imposed by regulators.

Nonlinear Time-Series Prediction with Missing and Noisy Data

1998 ◽  
Vol 10 (3) ◽  
pp. 731-747 ◽  
Author(s):  
Volker Tresp ◽  
Reimar Hofmann
Keyword(s):  
Time Series ◽  
Stochastic Simulation ◽  
Time Series Prediction ◽  
Noisy Data ◽  
Nonlinear Time Series ◽  
Point Of View ◽  
Data Set ◽  
Sunspot Data ◽  
Error Bars ◽  
Probabilistic Point

We derive solutions for the problem of missing and noisy data in nonlinear time-series prediction from a probabilistic point of view. We discuss different approximations to the solutions—in particular, approximations that require either stochastic simulation or the substitution of a single estimate for the missing data. We show experimentally that commonly used heuristics can lead to suboptimal solutions. We show how error bars for the predictions can be derived and how our results can be applied to K-step prediction. We verify our solutions using two chaotic time series and the sunspot data set. In particular, we show that for K-step prediction, stochastic simulation is superior to simply iterating the predictor.

scholarly journals An Interval of No-Arbitrage Prices in Financial Markets with Volatility Uncertainty

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Hanlei Hu ◽  
Zheng Yin ◽  
Weipeng Yuan
Keyword(s):  
Brownian Motion ◽  
Financial Markets ◽  
Stock Price ◽  
Contingent Claims ◽  
Price Dynamics ◽  
Complex Situation ◽  
No Arbitrage ◽  
Price Process ◽  
Arbitrage Opportunities

In financial markets with volatility uncertainty, we assume that their risks are caused by uncertain volatilities and their assets are effectively allocated in the risk-free asset and a risky stock, whose price process is supposed to follow a geometric G-Brownian motion rather than a classical Brownian motion. The concept of arbitrage is used to deal with this complex situation and we consider stock price dynamics with no-arbitrage opportunities. For general European contingent claims, we deduce the interval of no-arbitrage price and the clear results are derived in the Markovian case.

Survey of Trading Systems for Individual Investors

2011 ◽  
pp. 157-176 ◽  
Author(s):  
M. Kersch ◽  
G. Schmidt
Keyword(s):  
Financial Markets ◽  
Stock Exchange ◽  
Point Of View ◽  
Individual Investors ◽  
Individual Investor ◽  
Trading System ◽  
Trading Systems ◽  
Trading Decisions ◽  
The Individual

Trading decisions in financial markets can be supported by the use of trading algorithms. To evaluate trading algorithms and to generate orders to be executed on the stock exchange trading systems are used. In this chapter, we define the individual investors’ requirements on a trading system, and analyze 17 trading systems from an individual investor’s point of view. The results of our study point out that the best alternative for an individual investor is not one single trading system, but a combination of two different classes of trading systems.

Die Stabilität von Finanzmärkten:Wie kann die Wirtschaftspolitik Vertrauen schaffen?

2006 ◽  
Vol 55 (1) ◽  
Author(s):  
Theresia Theurl ◽  
Jan Pieter Krahnen ◽  
Thomas P. Gehrig
Keyword(s):  
Credit Risk ◽  
Financial Markets ◽  
Financial Market ◽  
Financial Institutions ◽  
Banking Sector ◽  
Public Awareness ◽  
Credit Derivatives ◽  
Point Of View ◽  
Regulatory Oversight ◽  
The Creation

AbstractFrom Theresia Theurl’s point of view financial markets exhibit certain features that turn them inherently unstable. Therefore, economic policy measures were necessary and advisable, but they should not take the shape of isolated and selected interventions. Rather, these measures of financial market supervision and regulation had to be integrated into a comprehensive concept of micro- and macroeconomic policy in order to allow the creation of stabilizing trust.In his contribution, Jan Pieter Krahnen maintains, that the systemic risk of banks and financial institutions has changed and risen in recent years. According to his view, this is due to a more widespread use of credit derivatives. Although they may cause a more efficient distribution of credit risk in the banking sector, at the same time they could mean a higher vulnerability of the banking sector to system-wide contagion effects of credit risk. As such, financial market supervision as well as the Basel II rules on Capital Standards should take into account not only the credit risk exposure of individual financial institutions, but also correlation measures of their share prices.For Thomas Gehrig, empirical anomalies demonstrate the relevance of awareness and trust in financial markets. This note would argue in favor of social policies that enhance public awareness in financial markets as a basis for trust. And so naturally, these policies need to be complemented by a strong financial order that aims at minimizing behavioral risks. He says, trust requires a regulatory framework that reduces manipulation by private as well as public interests. A competitive order complemented by strong regulatory oversight may go a long way towards generating liquid financial markets and the creation of trust. Trust by individuals, however, would be most strongly encouraged when individuals are entrusted in managing their own financial market activities including their own pension arrangements.

scholarly journals A Neowicksellian in a New Classical World: The Methodology of Michael Woodford's Interest and Prices

2006 ◽  
Vol 28 (2) ◽  
pp. 143-149 ◽  
Author(s):  
Kevin D. Hoover
Keyword(s):  
Monetary Policy ◽  
Interest Rate ◽  
Financial Markets ◽  
Interest Rates ◽  
Theoretical Orientation ◽  
Central Banks ◽  
Point Of View ◽  
Monetary Aggregates ◽  
Classical World ◽  
Interest Rate Rule

Michael Woodford's Interest and Prices: Foundations of a Theory of Monetary Policy (2003) is an important book. Woodford's title is, of course, a conscious revival of Wicksell's own famous work and it points to an effort to recast the analysis of monetary policy as centered on interest rates. I believe that Woodford's theoretical orientation is essentially correct. In repairing to Wicksell, he places the monetary aggregates into a more reasonable perspective, correcting the distortions of the monetarist and Keynesian diversions with respect to money. My money is, so to speak, where my mouth is: My own textbook-in-progress is also based around an IS/interest-rate rule/AS model, in which financial markets cleared by price rather than the LM curve are emphasized. Such an approach, as Woodford notes, has become standard in central banks, but has not yet captured either core undergraduate or graduate textbooks and instruction. My task here, however, was not to praise Woodford's economics nor to trace or evaluate its Wicksellian routes, but to consider Interest and Prices from a methodological point of view.

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