Annual Report 2017 17Th Year of Operations
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Martingale Methods in Financial Modelling
Marek Musiela Marek Rutkowski Martingale Methods in Financial Modelling Second Edition Springer Table of Contents Preface to the First Edition V Preface to the Second Edition VII Part I. Spot and Futures Markets 1. An Introduction to Financial Derivatives 3 1.1 Options 3 1.2 Futures Contracts and Options 6 1.3 Forward Contracts 7 1.4 Call and Put Spot Options 8 1.4.1 One-period Spot Market 10 1.4.2 Replicating Portfolios 11 1.4.3 Maxtingale Measure for a Spot Market 12 1.4.4 Absence of Arbitrage 14 1.4.5 Optimality of Replication 15 1.4.6 Put Option 18 1.5 Futures Call and Put Options 19 1.5.1 Futures Contracts and Futures Prices 20 1.5.2 One-period Futures Market 20 1.5.3 Maxtingale Measure for a Futures Market 22 1.5.4 Absence of Arbitrage 22 1.5.5 One-period Spot/Futures Market 24 1.6 Forward Contracts 25 1.6.1 Forward Price 25 1.7 Options of American Style 27 1.8 Universal No-arbitrage Inequalities 32 2. Discrete-time Security Markets 35 2.1 The Cox-Ross-Rubinstein Model 36 2.1.1 Binomial Lattice for the Stock Price 36 2.1.2 Recursive Pricing Procedure 38 2.1.3 CRR Option Pricing Formula 43 X Table of Contents 2.2 Martingale Properties of the CRR Model 46 2.2.1 Martingale Measures 47 2.2.2 Risk-neutral Valuation Formula 50 2.3 The Black-Scholes Option Pricing Formula 51 2.4 Valuation of American Options 56 2.4.1 American Call Options 56 2.4.2 American Put Options 58 2.4.3 American Claim 60 2.5 Options on a Dividend-paying Stock 61 2.6 Finite Spot Markets 63 2.6.1 Self-financing Trading Strategies 63 2.6.2 Arbitrage Opportunities 65 2.6.3 Arbitrage Price 66 2.6.4 Risk-neutral Valuation Formula 67 2.6.5 Price Systems 70 2.6.6 Completeness of a Finite Market 73 2.6.7 Change of a Numeraire 74 2.7 Finite Futures Markets 75 2.7.1 Self-financing Futures Strategies 75 2.7.2 Martingale Measures for a Futures Market 77 2.7.3 Risk-neutral Valuation Formula 79 2.8 Futures Prices Versus Forward Prices 79 2.9 Discrete-time Models with Infinite State Space 82 3. -
An Empirical Investigation of the Black- Scholes Call
International Journal of BRIC Business Research (IJBBR) Volume 6, Number 2, May 2017 AN EMPIRICAL INVESTIGATION OF THE BLACK - SCHOLES CALL OPTION PRICING MODEL WITH REFERENCE TO NSE Rajesh Kumar 1 and Rachna Agrawal 2 1Research Scholar, Department of Management Studies 2Associate Professor, Department of Management Studies YMCA University of Science and Technology, Faridabad, Haryana, India ABSTRACT This paper investigates the efficiency of Black-Scholes model used for valuation of call option contracts written on Eight Indian stocks quoted on NSE. It has been generally observed that the B & S Model misprices options considerably on several occasions and the volatilities are ‘high for options which are highly overpriced. Mispriced worsen with the increased in volatility of the underlying stocks. In most of cases options are also highly underpriced by the model. In this research paper, the theoretical options prices of Nifty stock call options are calculated under the B & S Model. These theoretical prices are compared with the actual quoted prices in the market to gauge the pricing accuracy. KEYWORDS Black-Scholes Model, standard deviation, Mean Error, Root Mean Squared Error, Thiel’s Inequality coefficient etc. 1. INTRODUCTION An effective security market provides three principal opportunities- trading equities, debt securities and derivative products. For the purpose of risk management and trading, the pricing theories of stock options have occupied important place in derivative market. These theories range from relatively undemanding binomial model to more complex B & S Model (1973). The Black-Scholes option pricing model is a landmark in the history of Derivative. This preferred model provides a closed analytical view for the valuation of European style options. -
Introduction to Black's Model for Interest Rate
INTRODUCTION TO BLACK'S MODEL FOR INTEREST RATE DERIVATIVES GRAEME WEST AND LYDIA WEST, FINANCIAL MODELLING AGENCY© Contents 1. Introduction 2 2. European Bond Options2 2.1. Different volatility measures3 3. Caplets and Floorlets3 4. Caps and Floors4 4.1. A call/put on rates is a put/call on a bond4 4.2. Greeks 5 5. Stripping Black caps into caplets7 6. Swaptions 10 6.1. Valuation 11 6.2. Greeks 12 7. Why Black is useless for exotics 13 8. Exercises 13 Date: July 11, 2011. 1 2 GRAEME WEST AND LYDIA WEST, FINANCIAL MODELLING AGENCY© Bibliography 15 1. Introduction We consider the Black Model for futures/forwards which is the market standard for quoting prices (via implied volatilities). Black[1976] considered the problem of writing options on commodity futures and this was the first \natural" extension of the Black-Scholes model. This model also is used to price options on interest rates and interest rate sensitive instruments such as bonds. Since the Black-Scholes analysis assumes constant (or deterministic) interest rates, and so forward interest rates are realised, it is difficult initially to see how this model applies to interest rate dependent derivatives. However, if f is a forward interest rate, it can be shown that it is consistent to assume that • The discounting process can be taken to be the existing yield curve. • The forward rates are stochastic and log-normally distributed. The forward rates will be log-normally distributed in what is called the T -forward measure, where T is the pay date of the option. -
BANCA SELLA S.P.A. (Incorporated with Limited Liability Under the Laws of the Republic of Italy) €1,000,000,000 Euro Medium Term Note Programme
Base Prospectus BANCA SELLA S.p.A. (incorporated with limited liability under the laws of the Republic of Italy) €1,000,000,000 Euro Medium Term Note Programme This document has been approved as a base prospectus (the “Base Prospectus”) issued in compliance with Directive 2003/71/EC (as amended, to the extent such amendments have been implemented in the relevant Member State of the European Economic Area, the “Prospectus Directive”) by the Commission de Surveillance du Secteur Financier (the “CSSF”) in its capacity as competent authority under the Loi relative aux prospectus pour valeurs mobilières dated 10 July 2005 which implements the Prospectus Directive in Luxembourg (the “Luxembourg Prospectus Law”). Application has been made by Banca Sella S.p.A. (the “Issuer”) for notes (“Notes”) issued under the €1,000,000,000 Euro Medium Term Note Programme (the “Programme”) described in this Base Prospectus during the period of twelve months after the date hereof, being the approval date of this Base Prospectus, to be listed on the official list and admitted to trading on the regulated market of the Luxembourg Stock Exchange, which is a regulated market for the purposes of the Markets in Financial Instruments Directive 2004/39/EC (each such regulated market being a “Regulated Market”). The Programme also allows for Notes to be unlisted or to be admitted to listing, trading and/or quotation by such other or further competent authorities, stock exchanges and/or quotation systems as may be agreed with the Issuer. There are certain risks relating to the Issuer and the Notes which potential investors should ensure they fully understand. -
BANCA MEDIOLANUM SUSTAINABILITY 2019 “Our Bank Is Different from the Others Because We Focus on People: We Have Always Been a Bank Made of People, for People.”
BANCA MEDIOLANUM SUSTAINABILITY 2019 “ Our bank is different from the others because we focus on people: we have always been a bank made of people, for people.” Ennio Doris Chairman of Banca Mediolanum S.p.A. SUSTAINABILITY 2019 1 Contents 5 Letter from the CEO to Stakeholders 42 Environmental 10 The Values of Banca Mediolanum 12 Scope of the Group Commitment 14 Sustainability Scenario and Initiatives 19 The Materiality Matrix for the Environment 19 Sustainable Business 24 Capital Solidity and Stability 45 Environmental Protection 26 Innovation 45 Efforts and Actions for Reducing Consumption and Emissions 30 Governance 54 Social Corporate Governance, Corporate Identity Personnel, Customers and Responsible Business and the Community 33 Sustainability Governance 57 Collaborators 33 Sustainability Policy 57 Employees 34 Environmental Policy 60 Company Welfare Services 34 Management of Risks envisaged by 61 Family Banker Network Legislative Decree 254/2016 (ESG) 64 Customers 34 ESG Project Scoring 65 Customer-oriented communication 35 Code of Ethics and cultural initiatives 36 Commitment to Combating 69 ISO20121 Sustainability Events Corruption 70 Financial inclusion 38 Human Rights 72 Financial Education 40 Cybersecurity and Data Protection 72 Community 40 Transparency 75 Mediolanum Foundation NPO 41 Supplier Sourcing Process and Purchasing Methods 79 Find Out More 2 MEDIOLANUM GROUP SUSTAINABILITY 2019 3 Introduction Letter from the CEO to Stakeholders This document reports on Sustainability for the Mediolanum Group, specifying the actions, projects and policies pursued over the year 2019. Reporting is organized around the three main pillars given by Environmental, Social and Governance (ESG) principles, which in this case go beyond the scope of purely economic/financial concerns to explore three distinct spheres of social awareness. -
Annual Accounts and Report
Annual Accounts and Report as at 30 June 2018 WorldReginfo - 5b649ee5-9497-487a-9fdb-e60cdfc3179f LIMITED COMPANY SHARE CAPITAL € 443,521,470 HEAD OFFICE: PIAZZETTA ENRICO CUCCIA 1, MILAN, ITALY REGISTERED AS A BANK. PARENT COMPANY OF THE MEDIOBANCA BANKING GROUP. REGISTERED AS A BANKING GROUP Annual General Meeting 27 October 2018 WorldReginfo - 5b649ee5-9497-487a-9fdb-e60cdfc3179f www.mediobanca.com translation from the Italian original which remains the definitive version WorldReginfo - 5b649ee5-9497-487a-9fdb-e60cdfc3179f BOARD OF DIRECTORS Term expires Renato Pagliaro Chairman 2020 * Maurizia Angelo Comneno Deputy Chairman 2020 Alberto Pecci Deputy Chairman 2020 * Alberto Nagel Chief Executive Officer 2020 * Francesco Saverio Vinci General Manager 2020 Marie Bolloré Director 2020 Maurizio Carfagna Director 2020 Maurizio Costa Director 2020 Angela Gamba Director 2020 Valérie Hortefeux Director 2020 Maximo Ibarra Director 2020 Alberto Lupoi Director 2020 Elisabetta Magistretti Director 2020 Vittorio Pignatti Morano Director 2020 * Gabriele Villa Director 2020 * Member of Executive Committee STATUTORY AUDIT COMMITTEE Natale Freddi Chairman 2020 Francesco Di Carlo Standing Auditor 2020 Laura Gualtieri Standing Auditor 2020 Alessandro Trotter Alternate Auditor 2020 Barbara Negri Alternate Auditor 2020 Stefano Sarubbi Alternate Auditor 2020 * * * Massimo Bertolini Secretary to the Board of Directors www.mediobanca.com translation from the Italian original which remains the definitive version WorldReginfo - 5b649ee5-9497-487a-9fdb-e60cdfc3179f -
Annual Report
ANNUAL REPORT 2007 121st FINANCIAL YEAR SELLA HOLDING BANCA) SELLA ER M FOR ( Joint Stock Company Head Office in Biella – Share Capital and Reserves € 448.757.834 Member of the Deposit Guarantee Scheme Registered on the Banks and Banking Groups Roll Tax and VAT number 01709430027 13900 Biella (Italy) – via Italia, 2 Tel. 015.35011 – Telefax 015.351767 – Swift SELB IT 22 Web site www.gruppobancasella.it This volume has been printed on ecological recycled paper This volume has been printed on ecological recycled Insert: photographs from the Fondazione Sella archive Vittorio Sella, A crevasse on the Gabelhorn glacier, August 1, 1887 Vittorio Sella, Mischabelhörner seen from the North summit of Alphubel, August 3, 1887 Vittorio Sella, Lower summit of Monte Rosa in the direction of Macugnaga from the summit of Dufourspitze, August 11, 1887 Vittorio Sella, Cervino and Monte Rosa seen from somewhere near the Colle delle Grandes Murailles, September 18, 1887 CONTENTS BOARD OF DIRECTORS 7 BOARD OF STATUTORY AUDITORS 7 CHart OF BANCA SELLA GROUP 8 TERRITORIAL ORGANISATION OF BANCA SELLA GROUP 10 CORRESPONDENT BANKS FOR BANCA SELLA HOLDING 21 SHAREHOLDERS’ MEETING – NOTICE OF MEETING 23 BOARD OF DIRECTORS’ ANNUAL REPORT 25 Rating . 27 Financial highlights . 28 Alternative performance indicators follows . 29 Macroeconomic scenario . 30 Strategic issues and state of progress of three-year strategic plan . 33 Operating result . 34 Trade policies . 38 Operating performance in main areas of activity . 42 Operating structure . 47 Outlook . 50 Significant events occurred after the close of the financial year . 52 Own shares and shares of the parent company . 52 Equity investments and dealings with Group companies . -
Dixit-Pindyck and Arrow-Fisher-Hanemann-Henry Option Concepts in a Finance Framework
Dixit-Pindyck and Arrow-Fisher-Hanemann-Henry Option Concepts in a Finance Framework January 12, 2015 Abstract We look at the debate on the equivalence of the Dixit-Pindyck (DP) and Arrow-Fisher- Hanemann-Henry (AFHH) option values. Casting the problem into a financial framework allows to disentangle the discussion without unnecessarily introducing new definitions. Instead, the option values can be easily translated to meaningful terms of financial option pricing. We find that the DP option value can easily be described as time-value of an American plain-vanilla option, while the AFHH option value is an exotic chooser option. Although the option values can be numerically equal, they differ for interesting, i.e. non-trivial investment decisions and benefit-cost analyses. We find that for applied work, compared to the Dixit-Pindyck value, the AFHH concept has only limited use. Keywords: Benefit cost analysis, irreversibility, option, quasi-option value, real option, uncertainty. Abbreviations: i.e.: id est; e.g.: exemplum gratia. 1 Introduction In the recent decades, the real options1 concept gained a large foothold in the strat- egy and investment literature, even more so with Dixit & Pindyck (1994)'s (DP) seminal volume on investment under uncertainty. In environmental economics, the importance of irreversibility has already been known since the contributions of Arrow & Fisher (1974), Henry (1974), and Hanemann (1989) (AFHH) on quasi-options. As Fisher (2000) notes, a unification of the two option concepts would have the benefit of applying the vast results of real option pricing in environmental issues. In his 1The term real option has been coined by Myers (1977). -
Option Pricing: a Review
Option Pricing: A Review Rangarajan K. Sundaram Introduction Option Pricing: A Review Pricing Options by Replication The Option Rangarajan K. Sundaram Delta Option Pricing Stern School of Business using Risk-Neutral New York University Probabilities The Invesco Great Wall Fund Management Co. Black-Scholes Model Shenzhen: June 14, 2008 Implied Volatility Outline Option Pricing: A Review Rangarajan K. 1 Introduction Sundaram Introduction 2 Pricing Options by Replication Pricing Options by Replication 3 The Option Delta The Option Delta Option Pricing 4 Option Pricing using Risk-Neutral Probabilities using Risk-Neutral Probabilities The 5 The Black-Scholes Model Black-Scholes Model Implied 6 Implied Volatility Volatility Introduction Option Pricing: A Review Rangarajan K. Sundaram These notes review the principles underlying option pricing and Introduction some of the key concepts. Pricing Options by One objective is to highlight the factors that affect option Replication prices, and to see how and why they matter. The Option Delta We also discuss important concepts such as the option delta Option Pricing and its properties, implied volatility and the volatility skew. using Risk-Neutral Probabilities For the most part, we focus on the Black-Scholes model, but as The motivation and illustration, we also briefly examine the binomial Black-Scholes Model model. Implied Volatility Outline of Presentation Option Pricing: A Review Rangarajan K. Sundaram The material that follows is divided into six (unequal) parts: Introduction Pricing Options: Definitions, importance of volatility. Options by Replication Pricing of options by replication: Main ideas, a binomial The Option example. Delta The option delta: Definition, importance, behavior. Option Pricing Pricing of options using risk-neutral probabilities. -
Analysis of Employee Stock Options and Guaranteed Withdrawal Benefits for Life by Premal Shah B
Analysis of Employee Stock Options and Guaranteed Withdrawal Benefits for Life by Premal Shah B. Tech. & M. Tech., Electrical Engineering (2003), Indian Institute of Technology (IIT) Bombay, Mumbai Submitted to the Sloan School of Management in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Operations Research at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 2008 c Massachusetts Institute of Technology 2008. All rights reserved. Author.............................................................. Sloan School of Management July 03, 2008 Certified by. Dimitris J. Bertsimas Boeing Professor of Operations Research Thesis Supervisor Accepted by . Cynthia Barnhart Professor Co-director, Operations Research Center 2 Analysis of Employee Stock Options and Guaranteed Withdrawal Benefits for Life by Premal Shah B. Tech. & M. Tech., Electrical Engineering (2003), Indian Institute of Technology (IIT) Bombay, Mumbai Submitted to the Sloan School of Management on July 03, 2008, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Operations Research Abstract In this thesis we study three problems related to financial modeling. First, we study the problem of pricing Employee Stock Options (ESOs) from the point of view of the issuing company. Since an employee cannot trade or effectively hedge ESOs, she exercises them to maximize a subjective criterion of value. Modeling this exercise behavior is key to pricing ESOs. We argue that ESO exercises should not be modeled on a one by one basis, as is commonly done, but at a portfolio level because exercises related to different ESOs that an employee holds would be coupled. Using utility based models we also show that such coupled exercise behavior leads to lower average ESO costs for the commonly used utility functions such as power and exponential utilities. -
Sequential Compound Options and Investments Valuation
Sequential compound options and investments valuation Luigi Sereno Dottorato di Ricerca in Economia - XIX Ciclo - Alma Mater Studiorum - Università di Bologna Marzo 2007 Relatore: Prof. ssa Elettra Agliardi Coordinatore: Prof. Luca Lambertini Settore scienti…co-disciplinare: SECS-P/01 Economia Politica ii Contents I Sequential compound options and investments valua- tion 1 1 An overview 3 1.1 Introduction . 3 1.2 Literature review . 6 1.2.1 R&D as real options . 11 1.2.2 Exotic Options . 12 1.3 An example . 17 1.3.1 Value of expansion opportunities . 18 1.3.2 Value with abandonment option . 23 1.3.3 Value with temporary suspension . 26 1.4 Real option modelling with jump processes . 31 1.4.1 Introduction . 31 1.4.2 Merton’sapproach . 33 1.4.3 Further reading . 36 1.5 Real option and game theory . 41 1.5.1 Introduction . 41 1.5.2 Grenadier’smodel . 42 iii iv CONTENTS 1.5.3 Further reading . 45 1.6 Final remark . 48 II The valuation of new ventures 59 2 61 2.1 Introduction . 61 2.2 Literature Review . 63 2.2.1 Flexibility of Multiple Compound Real Options . 65 2.3 Model and Assumptions . 68 2.3.1 Value of the Option to Continuously Shut - Down . 69 2.4 An extension . 74 2.4.1 The mathematical problem and solution . 75 2.5 Implementation of the approach . 80 2.5.1 Numerical results . 82 2.6 Final remarks . 86 III Valuing R&D investments with a jump-di¤usion process 93 3 95 3.1 Introduction . -
Calibration Risk for Exotic Options
Forschungsgemeinschaft through through Forschungsgemeinschaft SFB 649DiscussionPaper2006-001 * CASE - Center for Applied Statistics and Economics, Statisticsand Center forApplied - * CASE Calibration Riskfor This research was supported by the Deutsche the Deutsche by was supported This research Wolfgang K.Härdle** Humboldt-Universität zuBerlin,Germany SFB 649, Humboldt-Universität zu Berlin zu SFB 649,Humboldt-Universität Exotic Options Spandauer Straße 1,D-10178 Berlin Spandauer http://sfb649.wiwi.hu-berlin.de http://sfb649.wiwi.hu-berlin.de Kai Detlefsen* ISSN 1860-5664 the SFB 649 "Economic Risk". "Economic the SFB649 SFB 6 4 9 E C O N O M I C R I S K B E R L I N Calibration Risk for Exotic Options K. Detlefsen and W. K. H¨ardle CASE - Center for Applied Statistics and Economics Humboldt-Universit¨atzu Berlin Wirtschaftswissenschaftliche Fakult¨at Spandauer Strasse 1, 10178 Berlin, Germany Abstract Option pricing models are calibrated to market data of plain vanil- las by minimization of an error functional. From the economic view- point, there are several possibilities to measure the error between the market and the model. These different specifications of the error give rise to different sets of calibrated model parameters and the resulting prices of exotic options vary significantly. These price differences often exceed the usual profit margin of exotic options. We provide evidence for this calibration risk in a time series of DAX implied volatility surfaces from April 2003 to March 2004. We analyze in the Heston and in the Bates model factors influencing these price differences of exotic options and finally recommend an error func- tional.