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Book description

This book is meant to build the solid mathematical foundation required to understand the quantitative models used financial engineering. The financial applications in the book range from basics such as the Put-Call parity, bond duration and convexity, and the Black-Scholes model, to more advanced topics, such as numerical estimation of the Greeks, implied volatility, and bootstrapping for finding interest rate curves. On the mathematical side, useful but sometimes overlooked topics are presented in detail: differentiating integrals with respect to nonconstant integral limits, numerical approximation of definite integrals, convergence of Taylor series expansions, finite difference approximations, Stirlings formula, Lagrange multipliers, polar coordinates, Newtons method for higher dimensional problems. Every chapter concludes with exercises that are a mix of mathematical and financial questions, with comments regarding their relevance to practice and to more advanced topics.

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