Efficient Methods for Valuing Interest Rate Derivatives (Springer Finance) Hardcover – 31 Jul 2000
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This book answers all of these questions in a straightforward yet rigorous manner. Explanations are supplemented with simple examples.
After reading this book, I had the roadmap and analytical context I needed to tackle implementation focused books like Brigo and Mercurio.
As a bonus, this book provides a very nice summary of major valuation tools. (Monte Carlo simulation of martingale processes, development of pricing PDE via Feynman-Kac, development of fundamental solutions, etc.)
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