European Option Pricing Under Fractional Brownian Motion with an Application to Realized Volatility

2015 ◽  
Author(s):  
Takayuki Morimoto
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Realized Volatility ◽  
European Option ◽  
European Option Pricing

scholarly journals European option pricing by using a mixed fractional Brownian motion

2018 ◽  
Vol 1097 ◽  
pp. 012081 ◽  
Author(s):  
C E Murwaningtyas ◽  
S H Kartiko ◽  
Gunardi ◽  
H P Suryawan
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
European Option ◽  
European Option Pricing ◽  
Mixed Fractional Brownian Motion

Fuzzy simulation of European option pricing using mixed fractional Brownian motion

2019 ◽  
Vol 23 (24) ◽  
pp. 13205-13213
Author(s):  
Sara Ghasemalipour ◽  
Behrouz Fathi-Vajargah
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Fuzzy Simulation ◽  
European Option ◽  
European Option Pricing ◽  
Mixed Fractional Brownian Motion

European Option Pricing under Fractional Stochastic Interest Rate Model

2010 ◽  
Vol 171-172 ◽  
pp. 787-790
Author(s):  
Wen Li Huang ◽  
Gui Mei Liu ◽  
Sheng Hong Li ◽  
An Wang
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Fractional Brownian Motion ◽  
Stock Price ◽  
Stochastic Interest Rate ◽  
European Option ◽  
European Option Pricing ◽  
Stochastic Interest ◽  
Pde Method ◽  
And Control

Under the assumption of stock price and interest rate obeying the stochastic differential equation driven by fractional Brownian motion, we establish the mathematical model for the financial market in fractional Brownian motion setting. Using the risk hedge technique, fractional stochastic analysis and PDE method, we obtain the general pricing formula for the European option with fractional stochastic interest rate. By choosing suitable Hurst index, we can calibrate the pricing model, so that the price can be used as the actual price of option and control the risk management

scholarly journals Option Pricing under Double Heston Jump-Diffusion Model with Approximative Fractional Stochastic Volatility

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 126
Author(s):  
Ying Chang ◽  
Yiming Wang ◽  
Sumei Zhang
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Stochastic Volatility ◽  
Heston Model ◽  
Pricing Models ◽  
Market Data ◽  
Nested Models ◽  
European Option Pricing ◽  
Jump Diffusion Model

Based on the present studies about the application of approximative fractional Brownian motion in the European option pricing models, our goal in the article is that we adopt the creative model by adding approximative fractional stochastic volatility to double Heston model with jumps since approximative fractional Brownian motion is more proper for application than Brownian motion in building option pricing models based on financial market data. We are the first to adopt the creative model. We derive the pricing formula for the options and the formula for the characteristic function. We also estimate the parameters with the loss function for the model and two nested models and compare the performance among those models based on the market data. The outcome illustrates that the model offers the best performance among the three models. It demonstrates that approximative fractional Brownian motion is more proper for application than Brownian motion.

European Option Pricing Problems with Fractional Uncertain Processes

2021 ◽  
Vol 143 ◽  
pp. 110606
Author(s):  
Gang Shi ◽  
Jinwu Gao
Keyword(s):  
Option Pricing ◽  
European Option ◽  
European Option Pricing ◽  
Pricing Problems

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

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