Paper Review:"New Insight into Smile, Mispricing, and Value at Risk: The Hyperbolic Model" by E' Ebe - PowerPoint PPT Presentation

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Paper Review:"New Insight into Smile, Mispricing, and Value at Risk: The Hyperbolic Model" by E' Ebe

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Title: Paper Review:"New Insight into Smile, Mispricing, and Value at Risk: The Hyperbolic Model" by E' Ebe


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
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