scholarly journals Fractional Partial Differential Equations associated with L$\hat{e}$vy Stable Process

2020 ◽  
Author(s):  
Reem Abdullah Aljedhi ◽  
Adem Kilicman
Keyword(s):  
Diffusion Equation ◽  
Option Pricing ◽  
Stable Process ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
European Option ◽  
Fractional Partial Differential Equations ◽  
European Option Pricing ◽  
Risk Neutral ◽  
Time Fractional Diffusion Equation

In this study, we first present a time-fractional L$\hat{e}$vy diffusion equation of the exponential option pricing models of European option pricing and the risk-neutral parameter. Then, we modify a particular L$\hat{e}$vy-time fractional diffusion equation of European-style options. Introduce a more general model from the models based on the L$\hat{e}$vy-time fractional diffusion equation and review some recent findings regarding of the Europe option pricing of risk-neutral free.

scholarly journals Fractional Partial Differential Equations Associated with Lêvy Stable Process

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 508
Author(s):  
Reem Abdullah Aljedhi ◽  
Adem Kılıçman
Keyword(s):  
Diffusion Equation ◽  
Option Pricing ◽  
Stable Process ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
European Option ◽  
Fractional Partial Differential Equations ◽  
European Option Pricing ◽  
Risk Neutral ◽  
Time Fractional Diffusion Equation

In this study, we first present a time-fractional L e ^ vy diffusion equation of the exponential option pricing models of European option pricing and the risk-neutral parameter. Then, we modify a particular L e ^ vy-time fractional diffusion equation of European-style options. Further, we introduce a more general model based on the L e ^ vy-time fractional diffusion equation and review some recent findings associated with risk-neutral free European option pricing.

scholarly journals Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 796 ◽  
Author(s):  
Jean-Philippe Aguilar ◽  
Jan Korbel ◽  
Yuri Luchko
Keyword(s):  
Diffusion Equation ◽  
Option Pricing ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Model Parameters ◽  
Exotic Options ◽  
European Option ◽  
European Option Pricing ◽  
Space Fractional Diffusion Equation ◽  
Risk Neutral

In this article, we first provide a survey of the exponential option pricing models and show that in the framework of the risk-neutral approach, they are governed by the space-fractional diffusion equation. Then, we introduce a more general class of models based on the space-time-fractional diffusion equation and recall some recent results in this field concerning the European option pricing and the risk-neutral parameter. We proceed with an extension of these results to the class of exotic options. In particular, we show that the call and put prices can be expressed in the form of simple power series in terms of the log-forward moneyness and the risk-neutral parameter. Finally, we provide the closed-form formulas for the first and second order risk sensitivities and study the dependencies of the portfolio hedging and profit-and-loss calculations upon the model parameters.

Modeling of financial processes with a space-time fractional diffusion equation of varying order

2016 ◽  
Vol 19 (6) ◽  
Author(s):  
Jan Korbel ◽  
Yuri Luchko
Keyword(s):  
Diffusion Equation ◽  
Option Pricing ◽  
Real Option ◽  
Fractional Diffusion ◽  
Space Time ◽  
Fractional Diffusion Equation ◽  
Scaling Exponent ◽  
Option Prices ◽  
Scaling Properties ◽  
Time Fractional Diffusion Equation

AbstractIn this paper, a new model for financial processes in form of a space-time fractional diffusion equation of varying order is introduced, analyzed, and applied for some financial data. While the orders of the spatial and temporal derivatives of this equation can vary on different time intervals, their ratio remains constant and thus the global scaling properties of its solutions are conserved. In this way, the model covers both a possible complex short-term behavior of the financial processes and their long-term dynamics determined by its characteristic time-independent scaling exponent. As an application, we consider the option pricing and describe how it can be modeled by the space-time fractional diffusion equation of varying order. In particular, the real option prices of index S&P 500 traded in November 2008 are analyzed in the framework of our model and the results are compared with the predictions made by other option pricing models.

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