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With its emphasis on examples, exercises and calculations, this
book suits advanced undergraduates as well as postgraduates and
practitioners. It provides a clear treatment of the scope and
limitations of mean-variance portfolio theory and introduces
popular modern risk measures. Proofs are given in detail, assuming
only modest mathematical background, but with attention to clarity
and rigour. The discussion of VaR and its more robust
generalizations, such as AVaR, brings recent developments in risk
measures within range of some undergraduate courses and includes a
novel discussion of reducing VaR and AVaR by means of hedging
techniques. A moderate pace, careful motivation and more than 70
exercises give students confidence in handling risk assessments in
modern finance. Solutions and additional materials for instructors
are available at www.cambridge.org/9781107003675.
The Black Scholes option pricing model is the first and by far the
best-known continuous-time mathematical model used in mathematical
finance. Here, it provides a sufficiently complex, yet tractable,
testbed for exploring the basic methodology of option pricing. The
discussion of extended markets, the careful attention paid to the
requirements for admissible trading strategies, the development of
pricing formulae for many widely traded instruments and the
additional complications offered by multi-stock models will appeal
to a wide class of instructors. Students, practitioners and
researchers alike will benefit from the book's rigorous, but
unfussy, approach to technical issues. It highlights potential
pitfalls, gives clear motivation for results and techniques and
includes carefully chosen examples and exercises, all of which make
it suitable for self-study.
This book focuses specifically on the key results in stochastic
processes that have become essential for finance practitioners to
understand. The authors study the Wiener process and Ito integrals
in some detail, with a focus on results needed for the
Black-Scholes option pricing model. After developing the required
martingale properties of this process, the construction of the
integral and the Ito formula (proved in detail) become the
centrepiece, both for theory and applications, and to provide
concrete examples of stochastic differential equations used in
finance. Finally, proofs of the existence, uniqueness and the
Markov property of solutions of (general) stochastic equations
complete the book. Using careful exposition and detailed proofs,
this book is a far more accessible introduction to Ito calculus
than most texts. Students, practitioners and researchers will
benefit from its rigorous, but unfussy, approach to technical
issues. Solutions to the exercises are available online.
This book explains in simple settings the fundamental ideas of
financial market modelling and derivative pricing, using the
no-arbitrage principle. Relatively elementary mathematics leads to
powerful notions and techniques - such as viability, completeness,
self-financing and replicating strategies, arbitrage and equivalent
martingale measures - which are directly applicable in practice.
The general methods are applied in detail to pricing and hedging
European and American options within the Cox-Ross-Rubinstein (CRR)
binomial tree model. A simple approach to discrete interest rate
models is included, which, though elementary, has some novel
features. All proofs are written in a user-friendly manner, with
each step carefully explained and following a natural flow of
thought. In this way the student learns how to tackle new problems.
This book presents the mathematics that underpins pricing models
for derivative securities in modern financial markets, such as
options, futures and swaps. This new edition adds substantial
material from current areas of active research, such as coherent
risk measures with applications to hedging, the arbitrage interval
for incomplete discrete-time markets, and risk and return and
sensitivity analysis for the Black-Scholes model.
Recent years have seen a number of introductory texts which focus
on the applications of modern stochastic calculus to the theory of
finance, and on the pricing models for derivative securities in
particular. Some of these books develop the mathematics very
quickly, making substantial demands on the readerOs background in
advanced probability theory. Others emphasize the financial
applications and do not attempt a rigorous coverage of the
continuous-time calculus. This book provides a rigorous
introduction for those who do not have a good background in
stochastic calculus. The emphasis is on keeping the discussion
self-contained rather than giving the most general results
possible.
With its emphasis on examples, exercises and calculations, this
book suits advanced undergraduates as well as postgraduates and
practitioners. It provides a clear treatment of the scope and
limitations of mean-variance portfolio theory and introduces
popular modern risk measures. Proofs are given in detail, assuming
only modest mathematical background, but with attention to clarity
and rigour. The discussion of VaR and its more robust
generalizations, such as AVaR, brings recent developments in risk
measures within range of some undergraduate courses and includes a
novel discussion of reducing VaR and AVaR by means of hedging
techniques. A moderate pace, careful motivation and more than 70
exercises give students confidence in handling risk assessments in
modern finance. Solutions and additional materials for instructors
are available at www.cambridge.org/9781107003675.
Students and instructors alike will benefit from this rigorous,
unfussy text, which keeps a clear focus on the basic probabilistic
concepts required for an understanding of financial market models,
including independence and conditioning. Assuming only some
calculus and linear algebra, the text develops key results of
measure and integration, which are applied to probability spaces
and random variables, culminating in central limit theory.
Consequently it provides essential prerequisites to graduate-level
study of modern finance and, more generally, to the study of
stochastic processes. Results are proved carefully and the key
concepts are motivated by concrete examples drawn from financial
market models. Students can test their understanding through the
large number of exercises and worked examples that are integral to
the text.
The Black Scholes option pricing model is the first and by far the
best-known continuous-time mathematical model used in mathematical
finance. Here, it provides a sufficiently complex, yet tractable,
testbed for exploring the basic methodology of option pricing. The
discussion of extended markets, the careful attention paid to the
requirements for admissible trading strategies, the development of
pricing formulae for many widely traded instruments and the
additional complications offered by multi-stock models will appeal
to a wide class of instructors. Students, practitioners and
researchers alike will benefit from the book's rigorous, but
unfussy, approach to technical issues. It highlights potential
pitfalls, gives clear motivation for results and techniques and
includes carefully chosen examples and exercises, all of which make
it suitable for self-study.
This book focuses specifically on the key results in stochastic
processes that have become essential for finance practitioners to
understand. The authors study the Wiener process and Ito integrals
in some detail, with a focus on results needed for the
Black-Scholes option pricing model. After developing the required
martingale properties of this process, the construction of the
integral and the Ito formula (proved in detail) become the
centrepiece, both for theory and applications, and to provide
concrete examples of stochastic differential equations used in
finance. Finally, proofs of the existence, uniqueness and the
Markov property of solutions of (general) stochastic equations
complete the book. Using careful exposition and detailed proofs,
this book is a far more accessible introduction to Ito calculus
than most texts. Students, practitioners and researchers will
benefit from its rigorous, but unfussy, approach to technical
issues. Solutions to the exercises are available online.
This book explains in simple settings the fundamental ideas of
financial market modelling and derivative pricing, using the
no-arbitrage principle. Relatively elementary mathematics leads to
powerful notions and techniques - such as viability, completeness,
self-financing and replicating strategies, arbitrage and equivalent
martingale measures - which are directly applicable in practice.
The general methods are applied in detail to pricing and hedging
European and American options within the Cox-Ross-Rubinstein (CRR)
binomial tree model. A simple approach to discrete interest rate
models is included, which, though elementary, has some novel
features. All proofs are written in a user-friendly manner, with
each step carefully explained and following a natural flow of
thought. In this way the student learns how to tackle new problems.
From Measures to Ito Integrals gives a clear account of measure
theory, leading via L2-theory to Brownian motion, Ito integrals and
a brief look at martingale calculus. Modern probability theory and
the applications of stochastic processes rely heavily on an
understanding of basic measure theory. This text is ideal
preparation for graduate-level courses in mathematical finance and
perfect for any reader seeking a basic understanding of the
mathematics underpinning the various applications of Ito calculus.
Students and instructors alike will benefit from this rigorous,
unfussy text, which keeps a clear focus on the basic probabilistic
concepts required for an understanding of financial market models,
including independence and conditioning. Assuming only some
calculus and linear algebra, the text develops key results of
measure and integration, which are applied to probability spaces
and random variables, culminating in central limit theory.
Consequently it provides essential prerequisites to graduate-level
study of modern finance and, more generally, to the study of
stochastic processes. Results are proved carefully and the key
concepts are motivated by concrete examples drawn from financial
market models. Students can test their understanding through the
large number of exercises and worked examples that are integral to
the text.
The Black Scholes option pricing model is the first and by far the
best-known continuous-time mathematical model used in mathematical
finance. Here, it provides a sufficiently complex, yet tractable,
testbed for exploring the basic methodology of option pricing. The
discussion of extended markets, the careful attention paid to the
requirements for admissible trading strategies, the development of
pricing formulae for many widely traded instruments and the
additional complications offered by multi-stock models will appeal
to a wide class of instructors. Students, practitioners and
researchers alike will benefit from the book's rigorous, but
unfussy, approach to technical issues. It highlights potential
pitfalls, gives clear motivation for results and techniques and
includes carefully chosen examples and exercises, all of which make
it suitable for self-study.
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