scholarly journals Pricing of Equity Indexed Annuity under Fractional Brownian Motion Model

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Lin Xu ◽  
Guangjun Shen ◽  
Dingjun Yao
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Financial Time Series ◽  
High Water ◽  
Self Similarity ◽  
Brownian Motion Model ◽  
Pricing Problems ◽  
Market Driven ◽  
Point To Point ◽  
The Impact

Fractional Brownian motion with Hurst exponentH∈(1/2,1)is a good candidate for modeling financial time series with long-range dependence and self-similarity. The main purpose of this paper is to address the valuation of equity indexed annuity (EIA) designs under the market driven by fractional Brownian motion. As a result, this paper presents an explicit pricing expression for point-to-point EIA design and bounds for the pricing of high-water-marked EIA design. Some numerical examples are given to illustrate the impact of the parameters involved in the pricing problems.

scholarly journals Fractional Laplace motion

2006 ◽  
Vol 38 (02) ◽  
pp. 451-464 ◽  
Author(s):  
T. J. Kozubowski ◽  
M. M. Meerschaert ◽  
K. Podgórski
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Hydraulic Conductivity ◽  
Fractional Brownian Motion ◽  
Long Range ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Self Similarity ◽  
One Dimensional ◽  
Financial Time

Fractional Laplace motion is obtained by subordinating fractional Brownian motion to a gamma process. Used recently to model hydraulic conductivity fields in geophysics, it might also prove useful in modeling financial time series. Its one-dimensional distributions are scale mixtures of normal laws, where the stochastic variance has the generalized gamma distribution. These one-dimensional distributions are more peaked at the mode than is a Gaussian distribution, and their tails are heavier. In this paper we derive the basic properties of the process, including a new property called stochastic self-similarity. We also study the corresponding fractional Laplace noise, which may exhibit long-range dependence. Finally, we discuss practical methods for simulation.

scholarly journals Fractional Laplace motion

2006 ◽  
Vol 38 (2) ◽  
pp. 451-464 ◽  
Author(s):  
T. J. Kozubowski ◽  
M. M. Meerschaert ◽  
K. Podgórski
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Hydraulic Conductivity ◽  
Fractional Brownian Motion ◽  
Long Range ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Self Similarity ◽  
One Dimensional ◽  
Financial Time

Fractional Laplace motion is obtained by subordinating fractional Brownian motion to a gamma process. Used recently to model hydraulic conductivity fields in geophysics, it might also prove useful in modeling financial time series. Its one-dimensional distributions are scale mixtures of normal laws, where the stochastic variance has the generalized gamma distribution. These one-dimensional distributions are more peaked at the mode than is a Gaussian distribution, and their tails are heavier. In this paper we derive the basic properties of the process, including a new property called stochastic self-similarity. We also study the corresponding fractional Laplace noise, which may exhibit long-range dependence. Finally, we discuss practical methods for simulation.

Option pricing under the fractional stochastic volatility model

2021 ◽  
Vol 63 ◽  
pp. 123-142
Author(s):  
Yuecai Han ◽  
Zheng Li ◽  
Chunyang Liu
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Stochastic Volatility ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
European Call Option ◽  
Volatility Model ◽  
The Impact

We investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution method. Some numerical simulations are given to illustrate the impact of parameters on option prices, and the results of comparison with other models are presented. doi:10.1017/S1446181121000225

Fractal Dimensional Analysis in Financial Time Series

GIS Business ◽  
2016 ◽  
Vol 10 (6) ◽  
pp. 46-52
Author(s):  
S. J. Bhatt ◽  
H. V. Dedania ◽  
Vipul R. Shah
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Long Range ◽  
Financial Market ◽  
Financial Time Series ◽  
Local Market ◽  
Jones Index ◽  
Financial Time ◽  
Predictability Index

A predictability index for time series of a financial market vector consisting of chosen market parameters is suggested providing a measure of long range predictability of the market. It is based on fractional Brownian motion that includes Brownian motion as a particular case followed by the time series of financial market parameters. By analyzing respective time series, these indices are computed for parameters like volatility, FII investments in the local market, IIP numbers, CPI numbers, Dow Jones Index, different stock market indices, currency rates, and gold prices.

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