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Anatoliy Swishchuk “Lunch at the Lab” Talk February 10, 2005

Paper Review: "New Insight into Smile, Mispricing, and Value at Risk: The Hyperbolic Model" by E. Eberlein, U. Keller and K. Prause (1998). Anatoliy Swishchuk “Lunch at the Lab” Talk February 10, 2005. The Hyperbolic Density. Fitted Densities.

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Anatoliy Swishchuk “Lunch at the Lab” Talk February 10, 2005

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  1. Paper Review:"New Insight into Smile, Mispricing, and Value at Risk: The Hyperbolic Model" by E. Eberlein, U. Keller and K. Prause (1998). Anatoliy Swishchuk “Lunch at the Lab” Talk February 10, 2005

  2. The Hyperbolic Density

  3. Fitted Densities

  4. Modelling Financial Assets (The most general Form)

  5. The Hyperbolic Levy Motion is a Pure Jump Process

  6. Drawback of the Model

  7. Reformulation of the Model

  8. Solution of the Basic Model

  9. The Hyperbolic Model • Infinitely Divisible • A Levy Process (stationary and independent increments) • Moment generating function is

  10. Incomplete Market

  11. Martingale Approach

  12. Option Pricing

  13. Comparison of Option Prices

  14. Three-Dimensional Comparison

  15. Black-Scholes Implicit Volatilities

  16. Implicit Hyperbolic Volatility

  17. Characteristic Function for the Levy Process

  18. Martingale Measure

  19. The Price Measure (density)

  20. Choosing Parameter Theta

  21. Calculating Theta to Define Martingale Measure I.

  22. Calculating Theta to Define Martingale Measure II.

  23. Calculating Theta to Define Martingale Measure III.

  24. References I

  25. References II • Eberlein E, Keller U. (1995) Hyperbolic Distributions in Finance, Bernoulli, 1, 281-99.

  26. Thank You for Your Attention!

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