Alain Ruttiens - Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues

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This edition first published 2013
Copyright 2013 Alain Ruttiens

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Library of Congress Cataloging-in-Publication Data to follow

A catalogue record for this book is available from the British Library.

ISBN 978-1-118-51345-3 (hardback) ISBN 978-1-118-51347-7 (ebk)
ISBN 978-1-118-51348-4 (ebk) ISBN 978-1-118-51349-1 (ebk)

To Prof. Didier Marteau,
without whom this book would not exist

Foreword

The valuation and risk dimensions of financial instruments, and, to some extent, the way they behave, rest on a vast, complex set of mathematical models grouped into what is called quantitative finance. Today more than ever, it should be required that each and every one involved in financial markets or products has good command of quantitative finance. The problem is that the many books in this field are devoted either to a specific type of financial instruments, combining product description and quantitative aspects, or to a specific mathematical or statistical theory, or otherwise, with an impressive degree of mathematical formalism, which needs a high degree of competence in mathematics and quantitative methods. Alain Ruttiens' text is aiming to offer in a single book what should be needed to be known by a wide readership to master the quantitative finance at large. It covers, on the one hand, all the financial products, from the traditional spot instruments in forex, stocks, interest rates, and so on, to the most complex derivatives, and, on the other hand, the major quantitative tools designed to value them, and to assess their risk potentials. This book should therefore provide the best entry-level reference for anyone concerned in some way with financial markets and products to master their quantitative aspects, or to fill the gaps in areas with which they are less familiar.

At first sight, this ambitious objective seems hard to achieve, given the variety and the complexity of the materials it aims to cover. As a matter of fact, Alain recognizes that fulfilling such an objective implies sorting among a vast array of topics in a rather subjective way. Fortunately, the author had the chance to at least induce a positive bias in such a subjective selection by relying upon his experience as a market practitioner for more than 20 years. He furthermore treats this material in a clear, pedagogical way, requiring no prerequisites in the reader, except the basics of algebra and statistics.

Finally, the reader should appreciate the overall aim of Alain's book, allowing for useful comparisons some valuation methods appearing to be more robust and trustworthy than others and often warning against the lack of reliability of some quantitative models, due to the hypotheses on which they are built. This last point is all the more crucial after the recent financial crises, which were at least partially due to some inappropriate uses of quantitative models.

For all of these reasons, my expectation is that Alain's book should be a great success.

A.G. Malliaris
Loyola University, Chicago

Main Notations

B	bond price
c	coupon rate of a bond
C	convexity, or call price, in function of the context
cov(.)	covariance of (.)
d	dividend paid by a stock
D	duration
D t	discount factor relative to time t
E (.)	expected value of (.)
F	forward price, or future price (depends on the context)
FV	future value
-ibor	generic for LIBOR, EURIBOR, or any other inter-bank market rate
K	strike price of an option
kurtosis
M	month or million, depending on context
MD	modified duration
MtM	Marked to Market (= valued to the observed current market price)
drift of a stochastic process
N	total number of a series (integer number), or nominal (notional) amount (depends on the context)
(.)	Gaussian (normal) density distribution function
N (.)	Gaussian (normal) cumulative distribution function
P	put price
P {.}	probability of {.}
PV	present value
(.)	Poisson density distribution function
r	generic symbol for a rate of return
r f	risk-free return
(.)	correlation of (.)
skew	skewness
S	spot price of an asset (equity, currency, etc.), as specified by the context
STD(.)	standard deviation of (.)
volatility of a stochastic process
t	current time, or time in general (depends on the context)
t	initial time
T	maturity time
tenor, that is, time interval between current time t and maturity T