Stochastic Calculus for Finance

Business & Finance, Economics, Statistics, Nonfiction, Science & Nature, Mathematics
Cover of the book Stochastic Calculus for Finance by Marek Capiński, Ekkehard Kopp, Janusz Traple, Cambridge University Press
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Author: Marek Capiński, Ekkehard Kopp, Janusz Traple ISBN: 9781139564076
Publisher: Cambridge University Press Publication: August 23, 2012
Imprint: Cambridge University Press Language: English
Author: Marek Capiński, Ekkehard Kopp, Janusz Traple
ISBN: 9781139564076
Publisher: Cambridge University Press
Publication: August 23, 2012
Imprint: Cambridge University Press
Language: English

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 Itô 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 Itô 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 Itô 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.

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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 Itô 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 Itô 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 Itô 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.

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