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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

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Pricing via Arbitrage

The Central Limit Theorem

The Binomial model

More on Binomial models

Finite difference methods

Value-at-Risk - VaR

Introduction to probability theory

Stochastic integration

Partial parabolic differential equations and Feynman-Kac

The Black-Scholes-Merton model

American versus European options

Analytical pricing formulas for American options

Poisson processes and jump diffusion

Diffusion models in general

Hedging

Exotic Options

Volatility
Something about weather derivatives

A Practical guide to pricing

Pricing using deflators

Securities with dividends

Some Fixed-Income securities and Black-Scholes

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Jan Roman is Financial Engineer in the Quantitative Risk Modelling Group at Swedbank Robur Funds, where he specializes in risk model validation, focusing on all inputs to front office systems including interest rates and volatility structures. He has over 16 years financial markets experience mostly in financial modeling and valuation in derivatives environments. He has held positions as Head of Market and Credit Risk, Swedbank Markets, Senior Risk Analyst at the Swedish financial Supervisory Authority, Senior Developer at SunGard and Senior Developer, OMX Stockholm Exchange.

Jan is also Senior Lecturer, Malardaran University, Sweden, where he teaches Analytical finance and financial engineering. He holds a PhD in Theoretical Physics from Chalmers University of Technology.

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