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 Mälardaran 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:

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.

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 Malardalen University, it provides exhaustive coverage of vanilla and exotic mathematical finance applications for trading and risk management, combining rigorous theory with real market application.

Volume I - Equity Derivatives Markets, Valuation and Risk Management.

Coverage includes:

• The fundamentals of stochastic processes used in finance including the change of measure with Girsanov transformation and the fundamentals of probability throry.
• Discrete time models, such as various binomial models and numerical solutions to Partial Differential Equations (PDEs)
• Monte-Carlosimulations and Value-at-Risk (VaR)
• Continuous time models, such as Black-Scholes-Merton and similar with extensions
Arbitrage theory in discrete and continuous time models

Volume II - Interest Rate Derivative Markets, Valuation and Risk Management

Coverage includes:

• Interest Rates including negative interest rates
• Valuation and model most kinds of IR instruments and their definitions.
• Bootstrapping; how to create an interest curve from prices of traded instruments.
• The multi curve framework and collateral discounting
• Difference of bootstrapping for trading and IR Risk
• Models and risk with positive and negative interest rates.
• Risk measures of IR instruments
• Option Adjusted Spread and embedded optionality.
• Pricing theory, calibration and stochastic processes of interest rates
• Numerical methods; Binomial and trinomial trees, PDEs (Crank-Nicholson), Newton-Raphson in 2 dimension.
• Black models, Normal models and Market models
• Pricing before and after the credit crises and the multiple curve framework.
• Valuation with collateral agreements, CVA, DVA and FVA

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.

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 Malardalen University, it provides exhaustive coverage of vanilla and exotic mathematical finance applications for trading and risk management, combining rigorous theory with real market application.

Volume I Equity Derivatives Markets, Valuation and Risk Management.

Coverage includes:

• The fundamentals of stochastic processes used in finance including the change of measure with Girsanov transformation and the fundamentals of probability throry.
• Discrete time models, such as various binomial models and numerical solutions to Partial Differential Equations (PDEs)
• Monte-Carlosimulations and Value-at-Risk (VaR)
• Continuous time models, such as BlackScholes-Merton and similar with extensions
Arbitrage theory in discrete and continuous time models

Volume II Interest Rate Derivative Markets, Valuation and Risk Management

Coverage includes:

• Interest Rates including negative interest rates
• Valuation and model most kinds of IR instruments and their definitions.
• Bootstrapping; how to create an interest curve from prices of traded instruments.
• The multi curve framework and collateral discounting
• Difference of bootstrapping for trading and IR Risk
• Models and risk with positive and negative interest rates.
• Risk measures of IR instruments
• Option Adjusted Spread and embedded optionality.
• Pricing theory, calibration and stochastic processes of interest rates
• Numerical methods; Binomial and trinomial trees, PDEs (CrankNicholson), NewtonRaphson in 2 dimension.
• Black models, Normal models and Market models
• Pricing before and after the credit crises and the multiple curve framework.
• Valuation with collateral agreements, CVA, DVA and FVA

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 Fey…