The BSM Model and European Option Pricing

2016 ◽  
pp. 383-475
Author(s):  
Arlie O. Petters ◽  
Xiaoying Dong
Keyword(s):  
Option Pricing ◽  
European Option ◽  
European Option Pricing

scholarly journals Fractional Order Stochastic Differential Equation with Application in European Option Pricing

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Qing Li ◽  
Yanli Zhou ◽  
Xinquan Zhao ◽  
Xiangyu Ge
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Option Pricing ◽  
Memory Effect ◽  
Fractional Order ◽  
Mean Value ◽  
European Option ◽  
European Option Pricing ◽  
Proposed Model ◽  
Pricing Formula

Memory effect is an important phenomenon in financial systems, and a number of research works have been carried out to study the long memory in the financial markets. In recent years, fractional order ordinary differential equation is used as an effective instrument for describing the memory effect in complex systems. In this paper, we establish a fractional order stochastic differential equation (FSDE) model to describe the effect of trend memory in financial pricing. We, then, derive a European option pricing formula based on the FSDE model and prove the existence of the trend memory (i.e., the mean value function) in the option pricing formula when the Hurst index is between 0.5 and 1. In addition, we make a comparison analysis between our proposed model, the classic Black-Scholes model, and the stochastic model with fractional Brownian motion. Numerical results suggest that our model leads to more accurate and lower standard deviation in the empirical study.

scholarly journals European option pricing with transaction costs and stochastic volatility: an asymptotic analysis

2014 ◽  
Vol 80 (4) ◽  
pp. 981-1008 ◽  
Author(s):  
R. E. Caflisch ◽  
G. Gambino ◽  
M. Sammartino ◽  
C. Sgarra
Keyword(s):  
Asymptotic Analysis ◽  
Option Pricing ◽  
Transaction Costs ◽  
Stochastic Volatility ◽  
European Option ◽  
European Option Pricing
Sign in / Sign up

Export Citation Format

Share Document