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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!