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Market Models (Carol Alexander) -- This is one of the few books focusing on models for constructing realistic asset price paths rather than addressing the typical pricing problem under the assumption of geometric brownian motion. It's an excellent book on applied financial data analysis that should be in every quant's library. |
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Stochastic Calculus for Finance II (Steven E. Shreve) -- I'm a big fan of Shreve's books. His approach is rigorous yet very lucid. Technically, this book should probably be in the educational section but I consider it more of an intermediary text. |
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Stochastic Calculus for Finance I (Steven E. Shreve) -- This book can either be used as an introduction to the second volume or as a reference to clarify the continuous-time models of the second volume in the more intuitive discrete-time setting. In either case, it is advisable to get both of these books. |
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Monte Carlo Methods in Finance (Peter Jaeckel) -- Traditional asset pricing models are elegant but unrealistic and limited in scope. Most of today's interesting finance problems can no longer be solved analytically and practitioners leverage Monte Carlo methods to tackle these challenges. One of the key objectives of researchers in is to find methods that improve convergence and reduce the variance of results. Jaeckel's book is an instant classic. |
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Monte Carlo Methods in Financial Engineering (Paul Glasserman) -- This book uses a different style than Jaeckel but is equally effective in teaching the central features of Monte Carlo methods applied to finance. I recommend both of these texts. |
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Dynamic Hedging (Nassim Nicholas Taleb) -- Taleb is a well-known derivatives trader and the approach he takes in this book is very pragmatic. Instead of blindly relying on standard pricing models, Taleb puts a strong emphasis on understanding the limitations of each model and the practical implications of dynamic hedging in real markets with bid/ask spreads, transction costs, volatility smiles, and many other oddities that are not properly captured by the mathematical models. |
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Mathematical Methods For Foreign Exchange (Alexander Lipton) -- This is probably the most complete mathematical treatment of exotic foreign exchange products. |
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Interest-Rate Option Models (Riccardo Rebonato) -- A good intermediary text on interest rate models. |
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Pricing Financial Instruments: The Finite Difference Method (Domingo Tavella et al) -- The finite difference method complements Monte Carlo methods and Binomial trees for pricing derivatives. Particularly for American options, finite difference approaches have certain advantages over their Monte Carlo counterparts. |
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