scholarly journals How to Identify an Arbitrage of Type B on Capital Markets

2018 ◽  
Vol 4 (1) ◽  
pp. 41
Author(s):  
Leszek Zaremba
Keyword(s):  
Financial Market ◽  
Matrix Model ◽  
Stock Options ◽  
Listed Company ◽  
Point Of View ◽  
Type B ◽  
Period Matrix ◽  
Treasury Bills ◽  
Put Options ◽  
Black Scholes

We propose here a 1-period matrix model of a fraction of the Polish financial market (for our purposes it will suffice to focus on a fraction of the market) built up from the point of view of the Polish biggest listed company KGHM. Using this model we construct an arbitrage portfolio consisting of 5 different assets, namely shares of KGHM, Treasury bills and 3 kinds of stock options. We recall the concept of arbitrage of type A and type B (called also an arbitrage I and arbitrage II, resp.) and illustrate it with examples. To prove that an arbitrage is possible to conduct, we separately distinguish scenarios when options prices are determined by the Black-Scholes formula, and when they deviate from their theoretical values. We prove that in all those cases an arbitrage of type B can be conducted. Since our approach does not rely on the specifics of Poland as a country, it can be equally well implemented in any other country which offers Treasury bills, as well as call and put options on shares of selected companies (KGHM in the studied case). The purpose of this study is to encourage practitioners to conduct an arbitrage in their own country, especially in a case when call and put options are offered on a local OTC market.

scholarly journals Creation and Valuation of Instruments Compensating Lower Share Prices with the Help of Black–Scholes Formula

2017 ◽  
Vol 9 (1) ◽  
pp. 25-32
Author(s):  
Leszek Zaremba
Keyword(s):  
Financial Market ◽  
Matrix Model ◽  
Listed Company ◽  
Listed Companies ◽  
The Other ◽  
View Point ◽  
Investment Funds ◽  
Share Prices ◽  
Black Scholes ◽  
Period Model

Abstract In this paper, we present a 1-period model of the Polish financial market from the view point of KGHM, the Polish largest listed company that suffered huge declines in share prices from 125 PLN in August 2015 to 60 PLN in January 2015. Our goal is to show how KGHM might create a portfolio (with practically zero cost), which would fully compensate the abovementioned declines. The methodology presented below may be equally well employed by many other listed companies and investment funds, as well. We create here a matrix model of the Polish financial market and employ the Black-Scholes formula to valuate portfolios compensating potential declines of KGHM’s shares prices. To give more insight to practitioners wishing to apply the results presented here to other listed companies, we distinguish two cases. In one of them, volatility of KGHM’s share prices is 20%, and in the other case it equals 33%.

scholarly journals How to Profit From Declines of Share Prices without Shorting Them

2018 ◽  
Vol 4 (1) ◽  
pp. 10
Author(s):  
Leszek Zaremba
Keyword(s):  
Financial Market ◽  
Matrix Model ◽  
The Other ◽  
Financial Instruments ◽  
View Point ◽  
Share Prices ◽  
Short Sale ◽  
Black Scholes ◽  
Period Model

We present a 1-period model of the Polish financial market from the view point of the largest Polish company KGH, whose share prices declined from 119 PLN on June 1, 2015 to 68 PLN on December 2, 2015. Our goal is to show how KGHM might create portfolios (with practically zero cost), which would (almost) fully compensate these declines without, what is very important, short sale of KGHM’s shares. The presented methodology is equally suitable in any country for all those companies for which options on their shares are also tradable. We employ here a matrix model of a fraction of the Polish financial market and make use of the Black–Scholes formula to valuate 3 portfolios replicating 3 desired by KGHM, but not available on the market, financial instruments. To give more insight to the readers, we distinguish two cases. In one of them, volatility of KGHM’s share prices is 33%, and in the other case it equals 20%.

scholarly journals Two stock options at the races: Black–Scholes forecasts

2012 ◽  
Vol 12 (9) ◽  
pp. 1325-1333 ◽  
Author(s):  
G. Oshanin ◽  
G. Schehr
Keyword(s):  
Stock Options ◽  
Black Scholes

scholarly journals From Shareholder Value to CEO Power: The Paradox of the 1990s

2005 ◽  
Vol 9 (1) ◽  
pp. 7-47 ◽  
Author(s):  
Robert Boyer
Keyword(s):  
Financial Market ◽  
Moral Philosophy ◽  
Bargaining Power ◽  
Stock Options ◽  
Ceo Power ◽  
Economic Theories ◽  
Long Run ◽  
Legal Sanctions ◽  
Top Manager ◽  
Wage Earners

Why did CEO remuneration explode during the 1990s and persist at high levels, even after the Internet bubble burst? This article surveys the alternative explanations that have been given of this paradox, mainly by various economic theories with some extension to political science, business administration, social psychology, moral philosophy and network analysis. It is argued that the diffusion of stock options and financial market-related incentives, supposed to discipline managers, have entitled them to convert their intrinsic power into remuneration and wealth, both at micro and macro level. This is the outcome of a de facto alliance of executives with financiers, who have exploited the long-run erosion of wage earners' bargaining power. The article also discusses the possible reforms that could reduce the probability and the adverse consequences of CEO and top-manager opportunism: reputation, business ethic, legal sanctions, public auditing of companies, or a shift from a shareholder to a stakeholder conception.

scholarly journals A robust numerical solution to a time-fractional Black–Scholes equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. M. Nuugulu ◽  
F. Gideon ◽  
K. C. Patidar
Keyword(s):  
Finite Difference ◽  
Stock Options ◽  
Stochastic Dynamics ◽  
European Options ◽  
Numerical Convergence ◽  
Put Option ◽  
Implicit Finite Difference Scheme ◽  
Black Scholes ◽  
Implicit Finite Difference ◽  
Rigorous Mathematical Analysis

AbstractDividend paying European stock options are modeled using a time-fractional Black–Scholes (tfBS) partial differential equation (PDE). The underlying fractional stochastic dynamics explored in this work are appropriate for capturing market fluctuations in which random fractional white noise has the potential to accurately estimate European put option premiums while providing a good numerical convergence. The aim of this paper is two fold: firstly, to construct a time-fractional (tfBS) PDE for pricing European options on continuous dividend paying stocks, and, secondly, to propose an implicit finite difference method for solving the constructed tfBS PDE. Through rigorous mathematical analysis it is established that the implicit finite difference scheme is unconditionally stable. To support these theoretical observations, two numerical examples are presented under the proposed fractional framework. Results indicate that the tfBS and its proposed numerical method are very effective mathematical tools for pricing European options.

ON THE VALUATION OF DERIVATIVES WITH SNAPSHOT RESET FEATURES

2008 ◽  
Vol 11 (08) ◽  
pp. 905-941 ◽  
Author(s):  
ERIC C. K. YU ◽  
WILLIAM T. SHAW
Keyword(s):  
Convertible Bonds ◽  
Convertible Bond ◽  
Put Options ◽  
Risk Characteristics ◽  
Black Scholes ◽  
Barrier Type ◽  
Simple Change ◽  
Discontinuous Nature ◽  
Change Of Variable ◽  
Digital Options

We propose a general approach that requires only a simple change of variable that keeps the valuation of call and put options (convertible bonds) with strike (conversion) price resets two-dimensional in the classical Black–Scholes setting. A link between reset derivatives, compound options and "discrete barrier" type options, when there is one reset is then discussed, from which we analyze the risk characteristics of reset derivatives, which can be significantly different from their vanilla counterparts. We also generalize the prototype reset structure and show that the delta and gamma of a convertible bond with reset can both be negative. Finally, we show that the "waviness" property found in the delta and gamma of some reset derivatives is due to the discontinuous nature of the reset structure, which is closely linked to digital options.

WIGNER MEASURES AND MOLECULAR PROPAGATION THROUGH GENERIC ENERGY LEVEL CROSSINGS

2003 ◽  
Vol 15 (10) ◽  
pp. 1285-1317 ◽  
Author(s):  
CLOTILDE FERMANIAN KAMMERER
Keyword(s):  
Energy Transfer ◽  
Normal Form ◽  
Energy Level ◽  
Point Of View ◽  
Time Dependent ◽  
Type B ◽  
Unified Framework ◽  
Level Crossings ◽  
Normal Form Theorem ◽  
Uniformly Bounded

We study the time-dependent Schrödinger equation with matrix-valued potential presenting a generic crossing of type B, I, J or K in Hagedorn's classification. We use two-scale Wigner measures for describing the Landau–Zener energy transfer which occurs at the crossing. In particular, in the case of multiplicity 2 eigenvalues, we calculate precisely the change of polarization at the crossing. Our method provides a unified framework in which codimension 2, 3 or 5 crossings can be discussed. We recover Hagedorn's result for wave packets, from Wigner measure point of view, and extend them to any data uniformly bounded in L2. The proof is based on a normal form theorem which reduces the problem to an operator-valued Landau–Zener formula.

Introduction

2017 ◽  
Author(s):  
Roi Wagner
Keyword(s):  
Option Pricing ◽  
Cognitive Theory ◽  
Philosophy Of Mathematics ◽  
Mathematical Cognition ◽  
Point Of View ◽  
Current State ◽  
Mathematical Life ◽  
Black Scholes ◽  
Epistemological Position ◽  
Mathematical Interpretation

This book examines the force of mathematics, what this force builds on, and how it works in practice by discussing mathematics not only from the point of view of applications but also from the point of view of its production. It explores the function of mathematical statements, their epistemological position, consensus in mathematics, and mathematical interpretation and semiosis. It also considers the notion of embodied mathematical cognition as well as the limitations of the cognitive theory of mathematical metaphor in accounting for the formation of actual historical mathematical life worlds. This introduction provides an overview of the current state of the philosophy of mathematics and presents a vignette on option pricing to give a concrete example of how mathematics relates to its wider scientific and practical context, with particular emphasis on the Black-Scholes formula.

Variations in Course and Branching of Sciatic Nerve and it’s Relation to Pyriformis Syndrome

2021 ◽  
Vol 9 (4) ◽  
pp. 8156-8159
Author(s):  
Patel Dinesh K ◽  
◽  
Shinde Amol A ◽  
Keyword(s):  
Sciatic Nerve ◽  
Hip Replacement ◽  
Popliteal Fossa ◽  
Point Of View ◽  
Lower Limbs ◽  
Type B ◽  
Sacral Plexus ◽  
Type D ◽  
Variant Anatomy ◽  
Anatomy Teaching

Background: Sciatic nerve is a branch of sacral plexus. It passes below the pyriformis and divides in the popliteal fossa. Higher division and relation of sciatic nerve to pyriformis have been documented. Beaton and Anson have classified relation of sciatic nerve to pyriformis. The aim of this study is to find incidence of variant anatomy of sciatic nerve as per Beaton and Anson classification. Materials and methods: 48 formalin embalmed lower limbs used for regular anatomy teaching were used. Branching and course of sciatic nerve was observed in gluteal region,thigh and popliteal fossa. Observations: As per Beaton and Anson classification, we found 81.2% showed type A or normal arrangement. Type B variation was seen in 14.6% while 4.2% showed type D variation. Conclusion: Variations in branching of sciatic nerve and it’s relation to pyriformis muscle are important from point of view of Surgeons and Anaesthetists. Knowledge of these variations will help reducing block failures in cases of sciatica, pyriformis syndrome and hip replacement surgeries. KEY WORDS: Sciatic nerve, Sacral plexus, Pyriformis Syndrome, Hip replacement.

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