Paper Review:New Insight into Smile, Mispricing, and Value at Risk: The Hyperbolic Model by E. Eberlein, U. Keller and K

Paper Review:New Insight into Smile, Mispricing, and Value at Risk: The Hyperbolic Model by E. Eberlein, U. Keller and K

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## Paper Review:New Insight into Smile, Mispricing, and Value at Risk: The Hyperbolic Model by E. Eberlein, U. Keller and K

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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!