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A Didactic Note on Affine Stochastic Volatility Models

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 References

  1. Barndorff-Nielsen O., Shephard N.: Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics. Journal of the Royal Statistical Society, Series B 63, 167-241 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  2. Brockwell P.: Representations of continuous-time ARMA processes. Journal of Applied Probability 41A, 375-382 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  3. Carr P., Geman H., Madan D., Yor M.: Stochastic volatility for Lévy processes. Mathematical Finance 13, 345-382 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Carr P., Madan D.: Option valuation using the fast Fourier transform. The Journal of Computational Finance 2, 61-73 (1999)

    Google Scholar 

  5. Carr P., Wu L.: The finite moment log stable process and option pricing. The Journal of Finance 58, 753-777 (2003)

    Article  Google Scholar 

  6. Carr P., Wu L.: Time-changed Lévy processes and option pricing. Journal of Financial Economics 71, 113-141 (2004)

    Article  Google Scholar 

  7. Duffie D., Filipovic D., Schachermayer, W.: Affine processes and applications in finance. The Annals of Applied Probability 13 984-1053 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ethier S., Kurtz T.: Markov Processes. Characterization and Convergence. New York: Wiley 1986

    MATH  Google Scholar 

  9. Goll T., Kallsen J.: Optimal portfolios for logarithmic utility. Stochastic Processes and their Applications 89, 31-48 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  10. Heston S.: A closed-form solution for options with stochastic volatilities with applications to bond and currency options. The Review of Financial Studies 6, 327-343 (1993)

    Article  Google Scholar 

  11. Jacod J.: Calcul Stochastique et Problèmes de Martingales, volume 714 of Lecture Notes in Mathematics. Berlin: Springer 1979

    Google Scholar 

  12. Jacod J., Shiryaev A.: Limit Theorems for Stochastic Processes. Berlin: Springer, second edition 2003.

    MATH  Google Scholar 

  13. Jiang G., Knight J.: Estimation of continuous-time processes via the empirical characteristic function. Journal of Business & Economic Statistics, 20, 198-212 (2002)

    Article  MathSciNet  Google Scholar 

  14. Kallsen J.: Optimal portfolios for exponential Lévy processes. Mathematical Methods of Operations Research 51, 357-374 (2000)

    Article  MathSciNet  Google Scholar 

  15. Kallsen J.: Localization and σ-martingales. Theory of Probability and Its Applications 48, 152-163 (2004)

    Article  MathSciNet  Google Scholar 

  16. Kallsen J., Shiryaev A.: The cumulant process and Esscher’s change of measure. Finance & Stochastics 6, 397-428 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  17. Kallsen J., Shiryaev A.: Time change representation of stochastic integrals. Theory of Probability and Its Applications 46, 522-528 (2002)

    Article  MathSciNet  Google Scholar 

  18. Klüppelberg C., Lindner A., Maller R.: A continuous-time GARCH process driven by a Lévy process: Stationarity and second order behaviour. Journal of Applied Probability 41, 601-622 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  19. Protter, P.: Stochastic Integration and Differential Equations. Berlin: Springer, second edition 2004

    MATH  Google Scholar 

  20. Raible, S.: Lévy Processes in Finance: Theory, Numerics, and Empirical Facts. Dissertation Universität Freiburg 2000

    Google Scholar 

  21. Sato, K.: Lévy Processes and Infinitely Divisible Distributions. Cambridge: Cambridge University Press 1999

    MATH  Google Scholar 

  22. Schöbel R., Zhu, J.: Stochastic volatility with an Ornstein-Uhlenbeck process: An extension. European Finance Review, 3 23-46 (1999)

    Article  MATH  Google Scholar 

  23. Shiryaev, A.: Essentials of Stochastic Finance. Singapore: World Scientific 1999

    MATH  Google Scholar 

  24. Stein E., Stein J.: Stock price distributions with stochastic volatility: An analytic approach. The Review of Financial Studies 4, 727-752 (1991)

    Article  Google Scholar 

  25. Winkel M.: The recovery problem for time-changed Lévy processes. Preprint 2001.

    Google Scholar 

  26. Yu J.: Empirical characteristic function estimation and its applications. Econo-metric Reviews 23 93-123 (2004)

    Article  MATH  Google Scholar 

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Kallsen, J. (2006). A Didactic Note on Affine Stochastic Volatility Models. In: From Stochastic Calculus to Mathematical Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30788-4_18

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