An introduction to the mathematics of financial derivatives / Salih N. Neftci.

Financial derivatives : a brief introduction -- A primer on the arbitrage theorem -- Calculus in deterministic and stochastic environments -- Pricing derivatives : models and notation -- Tools in probability theory -- Martingales and martingale representations -- Differentiation in stochastic environments -- The Wiener process and rare events in financial markets -- Integration in stochastic environments : the Ito integral -- Ito's lemma -- The dynamics of derivative prices : stochastic differential equations -- Pricing derivative products : partial differential equations -- The Black-Scholes PDE : an application -- Pricing derivative products : equivalent martingale measures -- Equivalent martingale measures : applications -- New results and tools for interest-sensitive securities -- Arbitrage theorem in a new setting : normalization and random interest rates -- Modeling term structure and related concepts -- Classical and HJM approaches to fixed income -- Classical PDE analysis for interest rate derivatives -- Relating conditional expectations to PDEs -- Stopping times and American-type securities.