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1 Cahier de la Recherche de l ISC Paris CRISC numéro 15 : Dynamique des organisations 1 er trimestre

2 Conseil scientifique Liste des membres : BRESSON Yoland, Professeur d'économie, ancien doyen, Université Paris - Val de Marne Paris XII CUMENAL Didier, Directeur de la recherche, professeur de Management des Systèmes d'information, Doctorat ès sciences de gestion ESCH Louis, Professeur de Finance, Directeur académique d'hec Liège, Université de Liège HETZEL Patrick, Professeur à l Université de Limoges KUZNIK Florian, Recteur, économiste, Université d'economie de Katowice (Pologne) MORIN Marc, Professeur en management des ressources humaines, Doctorat d'etat PARIENTE Georges, Doyen de la recherche, professeur d'économie, Doctorat d'etat PESQUEUX Yvon, Professeur titulaire de la chaire Développement des Systèmes d'organisation au CNAM PORTNOFF André Yves, Directeur de l'observatoire de la Révolution de l'intelligence à Futuribles REDSLOB Alain, Professeur d'économie, ancien doyen de la faculté des Sciences Economiques de Paris II ZEFFERI Bruno, Directeur Cegos Dirigeants 2

3 Comité de lecture Liste des membres : AGARWAL Aman, Professor of Finance and Director of Indian Institute of Finance, Editor of Finance India CHEN Kevin C., California State University, Editor, International Journal of Business CLARK Ephraïm, University of Middlesex, U.K. DESPRES Charles, Directeur de l International Institute of Management du Conservatoire National des Arts et Métiers, Paris DOMINGUEZ Juan Luis, Professeur titulaire de la Chaire Economie Financière et Comptabilité, Faculté d économie et sciences de l entreprise, Université de Barcelone, Espagne JÄGER Johannes, Doyen de University of Applied Sciences, Vienne (Autriche), Lecturer Fachochschule des bfi Wien Gesellschaft m.b.h. KUMAR Andrej Professor, Holder of Chair Jean Monnet, Faculty of Economics, University of Ljubljlna, Slovenia PARLEANI Didier, Professeur de droit à l Université de Paris 1 Panthéon- Sorbonne PRIGENT Jean-Luc, Professeur de finance à l Université de Paris Cergy RYAN Joan, Professor of Global Banking and Finance at the European Business School, London, Grande-Bretagne SCHEINWBERGER Albert G., Professeur à l Université de Constance, Allemagne 3

4 CRISC déjà parus Cahier n 1 : Finance (Edité en avril 2002) Cahier n 2 : Marketing (Edité en septembre 2002) Cahier n 3 : Economie (Edité en mars 2003) Cahier n 4 : Contrôle de gestion (Edité en décembre 2003) Cahier n 5 : Droit (Edité en mai 2004) Cahier n 6 : Ressources humaines (Edité en juin 2004) Cahier n 7 : Les NTIC (Edité en septembre 2004) Cahier n 8 : Microstructures et marchés financiers (Edité en janvier 2005) Cahier n 9 : International (Edité en mai 2005) Cahier n 10 : Marketing : études et décisions managériales (Edité en septembre 2005) Cahier n 11 : Actes du colloque de ressources humaines du 24 novembre 2005 «La responsabilité sociétale de l entreprise : quel avenir pour la fonction RH?» (Edité en janvier 2006) 4

5 Cahier n 12 : Stratégie (Edité en mars 2006) Cahier n 13 : Normes IFRS (Edité en juillet 2006) Cahier n 14 : Corporate Governance (Edité en octobre 2006) Cahier n 15 : Dynamique des organisations (Edité au 1 er trimestre 2007) CRISC hors série Actes de la 3 ème Conférence Internationale de Finance IFC 3 (mars 2005) Cahier hors série n 1 Finance Cahier hors série n 2 Bourse Cahier hors série n 3 Formalisation et Modélisation CRISC prochainement disponibles CRISC n 16 : Actes du colloque IFC 4 (Parution 2 ème trimestre 2007) 5

6 EMEFIR Le Centre de Recherche de l ISC vous annonce la parution d une nouvelle Revue «EMEFIR», «Euro-Mediterranean Economics and Finance Review» qu il copublie avec l Université de Cergy-Pontoise et avec le soutien du REMEREG, Réseau Euro-Méditerranéen pour l Enseignement et la Recherche en Economie et en Gestion. Cette Revue trimestrielle dont le numéro 1, volume 2, vient de paraître, téléchargeable sur notre site, est destinée à faire connaître des travaux contemporains en provenance principalement des pays riverains de la Méditerranée. Un Comité scientifique prestigieux comportant des auteurs de réputation mondiale est chargé de l organisation des conférences et de la sélection des travaux. A compter du vol. 2 n 2 (avril 2007), nous publierons une sélection d articles reçus à l occasion de la Conférence IFC 4, qui s est tenue du 15 au 17 Mars, réunissant plus de 1,000 personnes, avec la participation des Prix Nobel James Heckman et Harry Marcovits. Tous les détails, informations et appels à communication figurent en français et en anglais sur notre site ou sur le site dédié - 6

7 Sommaire PARIENTE Georges p 8 Doyen de la recherche de l ISC Paris Editorial AZARIA Michel & BELLALAH Monder p 11 Dynamics of financial markets, information and risk management BRADFORD Marc p 46 Organisation matricielle dans la concentration bancaire et rigidités dans la dynamique des innovations financières : complémentarités entre grandes banques et «boutiques» indépendantes CUMENAL Didier p 59 Peut-on modéliser et simuler les changements d état de l organisation au cours du temps? LEVYNE Olivier p 91 La dynamique de croissance externe d une banque relève-t-elle d une logique financière spécifique? LOUFRANI Yvan p 111 L entreprise reconstituée MORIEZ David p 136 Dynamique organisationnelle et prospective : quand la prospective manque de perspective MORIN Marc p 171 Quelques apports du paradigme de la rationalité procédurale et limitée, versus rationalité instrumentale, à la théorie des organisations et à la compréhension des dynamiques décisionnelles SAMMON David & ADAM Frédéric p 223 Information Systems as change agents the case of a failed implementation in the Irish Health Service 7

8 Editorial Georges PARIENTE Docteur ès Sciences Economiques Doyen de la recherche à l ISC Paris Ce nouveau CRISC est consacré à la dynamique des organisations. En ces temps d accélération du progrès et des innovations, une évolution de plus en plus rapide touche toutes les formes d activités humaines. Des Etats aux entreprises, des marchés aux individus, les changements institutionnels se multiplient et se télescopent. C est donc une approche pluridisciplinaire que nous proposent ici les enseignants de l ISC Paris appartenant à tous nos pôles de recherche : finance, droit, marketing et bien sûr management. Le premier article de Michel AZARIA, professeur de marketing à l ISC Paris, et Mondher BELLALAH, professeur de finance associé à l ISC Paris s intéresse à la récente prolifération des innovations financières. Des nouveaux titres, de nouveaux marchés, de nouvelles stratégies de trading dynamique sont apparus et continuent à se développer. L article analyse particulièrement les marchés d options sur actions, les marchés d obligations et, en retenant les exemples du pétrole et du cacao, les marchés des matières premières. A partir de la distinction classique entre grandes banques à réseau et petites banques indépendantes, Marc BRADFORD, professeur de finance à l ISC Paris étudie la complexité croissante des besoins des clients que les grandes banques traditionnelles ne peuvent ou ne veulent plus assurer et qui est prise en charge par de nouvelles structures plus légères et plus spécialisées. Un nouveau cycle de concentration bancaire originale est sans doute déjà perceptible délaissant la fonction classique d intermédiation pour une fédération des petites structures avec un élargissement croissant de leurs portefeuilles d activités. Didier CUMENAL, Docteur en sciences de gestion et Directeur de la Recherche, professeur de management à l ISC Paris, aborde par une approche plus quantitative l évolution des organisations. Un nouveau modèle systémique est élaboré pour simuler le comportement d une organisation. Une approche dynamique permet de construire et surtout de comprendre le cheminement des causes entre le passé et le présent. La profession bancaire est de nouveau le terrain d application retenu par Olivier LEVYNE, Docteur en sciences économiques, professeur de finance 8

9 à l ISC Paris. La dynamique de croissance externe de cette profession ne dépend pas seulement de l actualisation des flux futurs, c'est-à-dire, pour une banque des dividendes normatifs, mais surtout aujourd hui des contraintes prudentielles et de l objectif des ratio Cooke et Bâle 2. D un point de vue juridique, le juriste social, Yvan LOUFRANI, professeur de droit du travail à l ISC Paris, démontre que, malgré les innombrables mutations technologiques (restructurations, fusions, externalisation, cessions, transferts) imposées par la globalisation du monde économique, les notions d unité économique et sociale ou d entité économique restent indispensables pour comprendre la mutation mais aussi la permanence des communautés de travail. David MORIEZ, professeur de Gestion des Ressources Humaines à l ISC Paris nous propose une approche contingente du leadership et une analyse prospective multidisciplinaire des relations de travail. Cela nous permet de comprendre les différences entre la dimension organique et la dimension biologique de l organisation qui nécessite de positionner la compétence à l intersection du triptyque : personnes, stratégie, cultures. Marc MORIN, professeur responsable du Département GRH à l ISC Paris analyse l apport du paradigme de la rationalité procédurale de H. Simon à la théorie des organisations et à l explication de la dynamique décisionnelle. Cela permet de lever l obstacle épistémologique de l ancien paradigme de la rationalité instrumentale ou substantive Enfin, David SAMMON, college lecturer et Frédéric ADAM, senior lecturer et visiting professor à l ISC Paris, tous deux à l University College de Cork (Irlande) étudient le projet d implantation d ERP (Enterprise Resources Panning,) à partir de l expérience du service de santé publique irlandais, entre 1997 et Un projet aussi important, touchant salariés sur des milliers de sites différents pendant dix ans est évidemment riche d enseignements. Il permet de comprendre que l implantation d un ERP doit être appréhendée comme un programme de véritable changement organisationnel et non comme une simple implantation de logiciel. Les entreprises qui n en ont pas conscience vont droit à l échec comme l illustre ce projet qui a été finalement arrêté et fait l objet d une enquête parlementaire Nous restons comme d habitude dans l attente de vos remarques et commentaires. Georges PARIENTE Doyen de la Recherche 9

10 10

11 AZARIA Michel 1 Docteur ès lettres, ESCP Professeur de marketing à l ISC Paris BELLALAH Monder 2 Docteur en Sciences de Gestion Professeur associé de Finance à l ISC Paris Dynamics of financial markets, information and risk management Abstract The last three decades have witnessed a proliferation of financial innovations. Roughly speaking, financial innovations seem to belong to two classes. First, there are the new securities and their markets such as traded and over-the counter commodity, equity and interest rate derivative assets. Second, there are dynamic trading strategies using these instruments. 1. Section 1 is an introduction to the dynamics of forward and futures markets dynamics. 2. Section 2 studies options and their pay-offs. It examines the main bounds on option prices. 3. Section 3 presents the trading characteristics of commodity contracts using the oil markets as an example. 4. Section 4 studies the main trading characteristics of commodity markets and instruments. The analysis focuses on the instruments in the International Petroleum Exchange. 5. Section 5 presents the trading characteristics of another commodity: Cocoa. 6. Section 6 illustrates the main trading characteristics of options. The analysis concentrates mainly on equity options. 7. Section 7 develops the trading characteristics of bonds and bond markets

12 Résumé Pendant les trente dernières années nous avons constaté une prolifération d innovations financières que l on peut classer en deux catégories : les nouveaux titres et les nouveaux marchés, tels que les produits dérivés sur taux d intérêt, et les stratégies de trading dynamiques portant sur ces instruments. Cette approche dynamique est au centre de cet article. Elle s applique aux marchés d option (section 2), aux marchés de matières premières à partir de l exemple du prix du pétrole (section 3 et 4) ou du cacao (section 5). Avant de s achever sur les principaux traits du trading sur options, principalement les options portant sur des actions (section 6) et les caractéristiques des obligations et des marchés d obligations. Introduction The last three decades have witnessed a proliferation of financial innovations. Roughly speaking, financial innovations seem to belong to two classes. First, there are the new securities and their markets such as traded and over-the counter commodity, equity and interest rate derivative assets. Second, there are dynamic trading strategies using these instruments. Traded derivative assets are standardized contracts which are listed on organized exchanges. Over-the-counter derivative assets are tailor-made to the investor's needs and are often written by investment banks. Examples of classic or standard financial assets and commodity contracts include forward contracts, futures contracts, swaps, warrants and standard calls and puts on a wide range of underlying instruments like stocks, equity indices, interest rates and currencies. Futures and options markets enable investors to manage price risk. A call gives the right to its holder to buy the underlying asset at a given price within or at a specified period of time. A put option gives the right to the buyer to sell the underlying asset at the strike price within or at a specified period of time. The prices of these financial instruments are fully transparent because they are constantly updated as trading occurs. Examples of commodity contracts are oil and cocoa. The global crude oil trade is unique among 12

13 physical commodities in its size and its complexity. The oil market is ultimately concerned with the transportation, processing and storage of a raw material but in the last 30 years it has gone through revolutionary changes with worldwide political and economic consequences. Trading instruments have evolved along with the market. Crude oil is now traded on world markets using the spot asset, physical forward contracts, futures contracts, options on futures contracts, swaps, warrants, etc. Although crude oil from each field is unique in quality, trading instruments refer to certain crudes with common characteristics, including West Texas Intermediate (WTI), Dubai, Alaska North Slope and Brent blend. Each of these crudes or blends defines a specific oil market. However, the markets are linked together through arbitrage. The history of cocoa dates back to the 6th century with its origins in the Amazon Basin. It was first brought to Europe in the 17th century as a luxury drink. Market users include the international cocoa trade, cocoa processors and chocolate manufacturers, managed futures fund, institutional investors and options specialists. Full cocoa-related statistics are published in the "Quarterly Bulletin of Cocoa Statistics" in the ICCO publications. The information concerns the gross crop, the net crop, grindings, surplus/deficit, total stocks and free stocks. The cocoa Futures contract was originally launched in The Cocoa Traded Options contract was launched in 1987 as a means of offering market participants even greater flexibility and choice in their underlying activities. These contracts are traded in London (LIFFE). Besides the commodity markets, financial markets have also developed over the years. Index options on stock indexes and stock index futures began trading in the United States in 1983 with the introduction of the S&P 100 contract on the Chicago Board Options Exchange. There are several types of bonds and bond options traded in organised and OTC markets. They include zero-coupon bonds, bonds with call provisions, putable bonds, convertible bonds, bonds with warrants attached, exchangeable bonds, etc. The main difference between futures contracts and forward contracts is that forward contracts are over-the-counter instruments which are non - standardized and are subject to counter-party risk. The futures contract is standardized marked to market at the end of each trading day and, due to the role of the clearinghouse, has no counterparty risk. Futures and forwards have been around for a long time. Real financial innovation came about with the rise of the sophisticated valuation techniques that made it possible to price options in a rigorous way. Besides the simple call and put options, we now have European and American style options, swpations, 13

14 Asian options, lookback options binary options, etc. In fact, the gamut of financial instruments available is limited only by the imagination of the financial engineers. The proliferation of these instruments suggests that they fulfil a need. It seems that this need is related to taxation, regulation and transaction costs as well as to the cost structure of the marketing networks and distribution channels. SECTION 1: AN INTRODUCTION TO THE DYNAMICS OF FORWARD AND FUTURES MARKETS Over the last three decades, the financial marketplace has lived through a wave of financial innovations and structural changes in the securities industry. In this chapter we will describe the financial innovations and sketch the background of why they were developed and how they are traded. A derivative is a generic term to encompass all financial transactions which are not directly traded in the primary physical market. It refers to a financial instrument to manage a given risk. The term includes forwards, futures, options, commodity contracts, etc. 1. What is a forward contract? A forward contract is the simplest and most basic hedging instrument. It is an agreement between two parties to set the price today for a transaction that will not be completed until a specified date in the future. For example, a forward contract for 1 million, to be delivered in 6 months, at a price of 5,30 Danish kroner (DKK) for one dollar. These terms oblige the seller of the contract at the end of 6 months to deliver 1 million for the price of 5.30 DKK per dollar. On the other hand, the buyer must accept delivery of 1 million and deliver DKK 5.3 million. The only way for the buyer or the seller to cancel the contract at a later date is to enter into a reverse forward contract with the same bank or another institution. However, a reverse contract implies a gain or a loss because the forward rate is likely to change as time passes. Forward rate contracts are flexible and allow for customized hedges since all the terms can be negociated with the counterparty. However, each side of the contract bears what is called text counterparty risk, that is, the risk that the other side defaults on the future commitments. That's why futures contracts are often preferred to forward contracts. 14

15 2. What is a futures contract? A future is an exchange-traded contract between a buyer and seller and the clearinghouse of a futures exchange to buy or sell a standard quantity and quality of a commodity at a specified future date and price. The clearinghouse acts as a counterparty in all transactions and is responsible for holding traders' surety bonds to guarantee that transactions are completed. A forward contract is an agreement to buy or sell an asset at a certain future time for a certain future price whereas a spot contract is an agreement to buy or sell an asset today. Forward contracts are traded in the over-the-counter market and usually involve a financial institution on one side of the deal and either a client or another financial institution on the other side of the deal. One party to the deal takes a long position and agrees to purchase the asset. The other party takes the short position and agrees to sell the asset. The agreed price in the forward contract is called the delivery price, which is chosen so that the value of the contract to both sides is equal to zero. Consequently, it costs nothing to enter into a forward agreement. 3. What are the specific features of futures markets? A futures contract is very similar to a forward contract. It is an agreement between two parties to buy or sell an asset at a certain time for a certain price. Futures contracts are traded on organised exchanges. To facilitate trading the exchange specifies certain standardized features of the contract and trading takes place in such a way that the exchange is the ultimate counterparty to each transaction. Futures contracts differ from forward contracts in two other ways. First of all, payments are made over the life of the contract in what is called marking to market. Secondly, most futures contracts are closed out before maturity. Like forward contracts, futures contracts are used to lock in the interest rate, exchange rate or commodity price. But, futures markets are organized in such a way that the counterparty risk of default is always completely eliminated because the clearinghouse steps in between a buyer and a seller, each time a deal is struck in the pit. The clearinghouse adopts the position of the buyer to every seller, and of the seller to every buyer, i.e. the clearinghouse keeps a zero net position. This means that every trader in the futures markets has obligations only to the clearinghouse, and has strong expectations that the clearinghouse will maintain its side of the bargain as well. The credibility of the system is maintained through the requirements of margin and daily settlements. The margin is a deposit in 15

16 the form of cash, government securities, and stock in the clearing corporation or letters of credit issued by an approved bank. The main purpose of the margin is to provide a safeguard to ensure that traders will honor their obligations. It is usually set to the maximum loss a trader can experience in a normal trading day. Daily settlements, called making to market, involve debiting the cash accounts of those whose positions lost money for the day and crediting the cash accounts of those whose positions earned money. The elimination of default risk has a cost, however. Futures contracts are standardized with respect to quantities and delivery dates and limited to frequently traded financial assets. Therefore, available futures contracts may not correspond perfectly to the risk to be hedged, thereby leaving hedgers with what is called basis risk and correlation risk, which cannot be fully eliminated. The organized futures markets have four important features: 1) the contracts are standardized, 2) trading is organized and centralized either in one physical location such as the trading pit or in a virtual location such as a computerized order book, 3) contracts are settled through the exchange's clearing house, 4) contracts are marked to market each day, which means that they are revalued according to their market value. Standardized Contracts Contract standardization is a key feature of organized exchanges that facilitates market liquidity. For example, when the Chicago Mercantile Exchange (CME) opened the International Money Market to trade foreign exchange futures, these contracts were patterned after the futures contracts for the commodities it had been trading for over a hundred years. Maturities are based on a regular cycle, often a quarterly cycle of March, June, September, and December. Each contract has a precise delivery date, such as the third Wednesday of March, June, September and December or the first business day following one of these Wednesdays. Trading deadlines and delivery dates are specified. For example, trading foreign currency futures on the CME stops two business days before the expiration date and delivery takes place on the second business day after the expiration date. Each futures contract corresponds to a given amount of the underlying asset. For example, the CME's yen contract is for 12,500,000 yen, the pound contract for 62,500 British pounds and the Swiss franc contract for 125,000 francs. 16

17 Public and Competitive Trading Procedures Only commission houses registered as member firms are allowed to trade on the exchanges. Anyone else who seeks access to the market must do so through a commission house by opening an account. All orders are then executed through the commission house. In most markets opening an account is subject to strict rules and to certain financial guarantees such as a deposit of cash or marketable securities. The Role of The Clearing House The role of the Clearing House is threefold. It records the existence of the contract; it manages settlement of day to day operations; and it guarantees delivery at the contract's maturity. Thus, there is no individual counterparty risk because all clients have the Clearing House as the ultimate counterparty. The modern system of clearing used today by almost all futures markets was developed in the United States about Most clearing houses are specific to each exchange, although some clearing corporations such as I.C.C.H. in London act on behalf of several markets. Their role is always the same. They act as third party guarantors to all futures contracts and they manage the financial implications associated with their guarantee. The role of the clearing house is essential for a smooth functioning futures market. Clients do not have to worry about the solvability of the commission house because it requires guarantees from its members. All contracts are with the financially impregnable clearing house and, thus, for a given type are strictly equivalent. This facilitates trading and fosters liquidity. To ensure its financial position the clearing house imposes a clearing margin on its members. A clearing margin is a deposit in the form of cash, government issued securities, stock in the clearing corporation, or letters of credit issued by an approved bank that clearing members leave with the clearing house. The size of the deposit is fixed by the clearing house based on the member's net position or on its long and short positions and it can be revised upward or downward at any time depending on how the clearing house feels the market is going. Clearing margins are calculated every day in an exercise similar to the way that clients are marked to market. They must be large enough to cover maximum fluctuations in futures prices. Since prices vary from day to day, initial margins may become inadequate if prices move strongly against one or more members. In this case, the clearing house can make a margin call against the deficient members. They then have one hour to effect a "wire transfer of funds". These funds will be included in the end of day settlement procedures when all accounts are marked to market. It is clear that much 17

18 care is taken to ensure the exchange's solvability and that the clearing house wields extensive power over its members. Margin Calls and Marking to Market Member commission houses require the same type of guarantees from their clients that the clearing house requires of them. In fact, the margins that commission houses require of their clients are often higher than the margins required by the clearing house, although the deposits represent only a small proportion of the total contract and are virtually costless since interest bearing treasury bonds can be used. Clients' accounts are marked to market at the end of each day and clients are subject to margin calls if their position deteriorates. Margins and daily marking to market make client defaults a rare occasion and reinforce the overall financial soundness of the exchange. Marking to market means that profits and losses are paid every day at the end of trading and is equivalent to closing out a contract each day, paying off losses or receiving gains, and writing a new contract. The procedure can best be illustrated by an example. On Tuesday morning an investor takes a long position in a euro futures contract at a price of USD At the end of the day the price has risen to USD Since the amount of the contract is 125,000 euros, the investor's gain is: (USD USD1.200) x 125,000 = USD625. He receives his USD625 and is the owner of a contract whose price is now USD On Wednesday evening the price has fallen to USD Therefore, he has to pay: (USD USD1.195) x 125,000 = USD1250 and he owns a contract whose price is now USD The margin procedure is straightforward. An initial margin is deposited when a position is taken on a futures contract. This initial margin is usually set high enough so that the cost and inconvenience of frequent small payments can be avoided as the futures price is marked to market each day. Small losses are simply deducted from the initial margin until a predetermined lower bound, called the maintenance margin, is reached. At this point, the commission house issues a margin call requesting the client to deposit the funds necessary to bring the margin back to the initial level. 18

19 SECTION 2: AN INTRODUCTION TO OPTIONS MARKETS 1. What are standard Options? Options are more flexible than forwards and futures in the sense that they provide the buyer with full protection against unfavourable outcomes but allow him the full benefits associated with favourable outcomes. This price to be paid for this win-win position is called the option premium. A standard or a vanilla option is a security that gives its holder the right to buy or sell the underlying asset within a specified period of time, at a given price, called the strike price, striking price or exercise price. The right to buy is a call and the right to sell is a put. A call is in-the-money when the underlying asset price is higher than the strike price. It is out-of-the-money if the underlying asset price is lower than the strike price. The call is at-themoney if the underlying asset price is equal to the strike price. A put is inthe-money when the underlying asset price is lower than the strike price. It is out-of-the-money if the underlying asset price is higher than the strike price. The put is at-the-money if the underlying asset price is equal to the strike price. These definitions apply at maturity and at each instant before expiration. A European style option can be exercised only on the last day of the contract, called the maturity date or the expiration date. An American style option can be exercised at any time during the contract's life. 2. The main bounds on option prices Recall that an option is a contract that gives its owner the right for a given period of time to buy or sell a given amount of an underlying asset at a fixed price, called the exercise price or the strike price. The underlying asset can be a financial security such as a stock or a bond, a financial commodity such as an interest rate or a currency or a physical commodity such as oil, gas, coffee and potatoes. If the right can be exercised at any time during the life of the option it is called an American option. If the right can be exercised only at the option's expiration date, it is called a European option. The right to buy is called a call. The right to sell is called a put. The buyer of the option pays the seller, or the writer, a certain sum, called the premium, for the right to buy or sell at the prescribed price. The characteristic elements of an option contract can be summed up as follows: - the nature of the transaction: call or put - the underlying asset - the amount of the underlying asset - the strike or exercise price - the expiration date - the premium 19

20 Before maturity the value of an option is a function of five parameters: the price of the underlying asset, the strike price, the risk-free rate of interest, the movements in the underlying asset prices (volatility) and the time remaining to maturity. Option prices move at each instant of time as a reaction to changes in the above parameters. At maturity, however, the value of the option is known. To value a simple option, we start with the option payoff at maturity. This pay-off provides also the option intrinsic value. The option premium corresponds to the intrinsic value and speculative value. At maturity, the price of European and American calls (c and C) and European and American puts (p and P) are given as C T = c T = Max[0, S T - K], P T = p T = Max[0, S T - K] Where K is the strike price, S is the underlying asset price and T is the option's maturity date. The boundary space refers to the largest range of possible option prices before expiration Boundary conditions for call options When the call holder exercises his option, he receives the difference between the underlying asset price and the strike price or zero, whichever is higher. Even if the price of the underlying is far below the strike price, the value of the option can never fall below zero. If the strike price is zero and the maturity date is infinite, the call can be exercised with zero cost. This gives the call holder the right to receive the underlying asset with zero cost. The value of this option must be equal to that of its underlying asset. Hence, the call price must be between these two limits, that is, between zero and the value of the underlying asset. Example Consider a call with K = 100 when S_T = 90. At maturity, the call buyer does not exercise his option because the value of the underlying is below the strike price. Thus, the option expires worthless. Hence, the payoff for the call buyer is : C T = Max[0, S T - K] = Max[0, ] = Max[0, -10] = 0 However, if S T = 110, the option will be exercised, which gives an immediate payoff of 10, or C T = Max[0, S T - K] = Max[0, ] = Max[0, 10] = 10 The call seller has a short position in the call. The value of this position at expiration is - C T = - c T = - Max[0, S T - K] 20

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