A Course in Financial Calculus
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A Course in Financial Calculus
A Course in
Financial Calculus
Alison Etheridge University of Oxford
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521890779 © Cambridge University Press 2002 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2002 eBook (EBL) ISBN-13 978-0-511-33725-3 ISBN-10 0-511-33725-6 eBook (EBL) ISBN-13 ISBN-10 paperback 978-0-521-89077-9 paperback 0-521-89077-2
Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
Contents
Preface 1 Single period models Summary 1.1 Some definitions from finance 1.2 Pricing a forward 1.3 The one-step binary model 1.4 A ternary model 1.5 A characterisation of no arbitrage 1.6 The risk-neutral probability measure Exercises Binomial trees and discrete parameter martingales Summary 2.1 The multiperiod binary model 2.2 American options 2.3 Discrete parameter martingales and Markov processes 2.4 Some important martingale theorems 2.5 The Binomial Representation Theorem 2.6 Overture to continuous models Exercises Brownian motion Summary 3.1 Definition of the process 3.2 L´ vy’s construction of Brownian motion e 3.3 The reflection principle and scaling 3.4 Martingales in continuous time Exercises Stochastic calculus Summary
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A Course in Financial Calculus
A Course in
Financial Calculus
Alison Etheridge University of Oxford
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521890779 © Cambridge University Press 2002 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2002 eBook (EBL) ISBN-13 978-0-511-33725-3 ISBN-10 0-511-33725-6 eBook (EBL) ISBN-13 ISBN-10 paperback 978-0-521-89077-9 paperback 0-521-89077-2
Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
Contents
Preface 1 Single period models Summary 1.1 Some definitions from finance 1.2 Pricing a forward 1.3 The one-step binary model 1.4 A ternary model 1.5 A characterisation of no arbitrage 1.6 The risk-neutral probability measure Exercises Binomial trees and discrete parameter martingales Summary 2.1 The multiperiod binary model 2.2 American options 2.3 Discrete parameter martingales and Markov processes 2.4 Some important martingale theorems 2.5 The Binomial Representation Theorem 2.6 Overture to continuous models Exercises Brownian motion Summary 3.1 Definition of the process 3.2 L´ vy’s construction of Brownian motion e 3.3 The reflection principle and scaling 3.4 Martingales in continuous time Exercises Stochastic calculus Summary
page vii 1 1 1 4 6 8 9 13 18 21 21 21