Analytical Finance is a comprehensive introduction to the financial engineering of equity and interest rate instruments for financial markets. Developed from notes from the author's many years in quantitative risk management and modeling roles, and then for the Financial Engineering course at Mälardalen University, it provides exhaustive coverage of vanilla and exotic mathematical finance applications for trading and risk management, combining rigorous theory with real market application. Coverage includes: . Date arithmetic's, quote types of interest rate instruments . The interbank market and reference rates, including negative rates. Valuation and modeling of IR instruments; bonds, FRN, FRA, forwards, futures, swaps, CDS, caps/floors and others . Bootstrapping and how to create interest rate curves from prices of traded instruments. Risk measures of IR instruments. Option Adjusted Spread and embedded options. The term structure equation, martingale measures and stochastic processes of interest rates; Vasicek, Ho-Lee, Hull-While, CIR. Numerical models; Black-Derman-Toy and forward induction using Arrow-Debreu prices and Newton-Raphson in 2 dimension. The Heath-Jarrow-Morton framework. Forward measures and general option pricing models. Black log-normal and, normal model for derivatives, market models and managing exotics instruments. Pricing before and after the financial crisis, collateral discounting, multiple curve framework, cheapest-to-deliver curves, CVA, DVA and FVA von Röman, Jan R. M.