© 2017

Analytical Finance: Volume II

The Mathematics of Interest Rate Derivatives, Markets, Risk and Valuation


Table of contents

  1. Front Matter
    Pages i-xxxi
  2. Jan R. M. Röman
    Pages 1-15
  3. Jan R. M. Röman
    Pages 17-29
  4. Jan R. M. Röman
    Pages 31-45
  5. Jan R. M. Röman
    Pages 47-164
  6. Jan R. M. Röman
    Pages 165-173
  7. Jan R. M. Röman
    Pages 175-225
  8. Jan R. M. Röman
    Pages 227-235
  9. Jan R. M. Röman
    Pages 237-259
  10. Jan R. M. Röman
    Pages 261-278
  11. Jan R. M. Röman
    Pages 279-290
  12. Jan R. M. Röman
    Pages 291-305
  13. Jan R. M. Röman
    Pages 307-317
  14. Jan R. M. Röman
    Pages 319-326
  15. Jan R. M. Röman
    Pages 327-332
  16. Jan R. M. Röman
    Pages 333-448
  17. Jan R. M. Röman
    Pages 449-462
  18. Jan R. M. Röman
    Pages 463-490
  19. Jan R. M. Röman
    Pages 491-497
  20. Jan R. M. Röman
    Pages 499-524

About this book


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-Carlo simulations 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


Financial risk management Fixed income instruments Financial derivatives Pricing interest rate instruments Stochastic processes Credit derivatives Nelson-Siegel model Option Adjusted Spread method Negative interest rates Convertible bonds Yield curves Bootstrapping Pricing theory Martingale measures Term structure models Exotic instruments Convertible bonds Multi-curve framework Credit Value Adjustment LIBOR Market Model

Authors and affiliations

  1. 1.VästeråsSweden

About the authors

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.


Bibliographic information

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