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 included, which, though elementary, has some novel features. All proofs are written in a user-friendly manner, with each step carefully explained and following a natural flow of thought. In this way the student learns how to tackle new problems.

Discrete Models of Financial Markets (Mastering Mathematical Finance) by Marek Capinski (2012-03-26) PDF

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