Building on the basic concepts through a careful discussion of covalence, (while adhering resolutely to sequences where possible), the main part of the book concerns the central topics of continuity, differentiation and integration of real functions. Throughout, the historical context in which the subject was developed is highlighted and particular attention is paid to showing how precision allows us to refine our geometric intuition. The intention is to stimulate the reader to reflect on the underlying concepts and ideas.

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...

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...

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...

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...