scholarly journals EVOLUTION OF AMERICAN OPTION VALUE FUNCTION ON A DIVIDEND PAYING STOCK UNDER JUMP-DIFFUSION PROCESSES

2017 ◽  
Vol 2 (3) ◽  
pp. 212-221
Author(s):  
Рехман ◽  
Nazir Rekhman ◽  
Хуссейн ◽  
Zakir Khusseyn ◽  
Али ◽  
...  
Keyword(s):  
Variational Inequalities ◽  
Value Function ◽  
Diffusion Processes ◽  
Equivalent Form ◽  
Jump Diffusion ◽  
American Option ◽  
Option Value ◽  
Jump Diffusion Processes ◽  
Hedging Strategies ◽  
The Value Function

This work is devoted to the analysis and evolution of the value function of American type options on a dividend paying stock under jump diffusion processes. An equivalent form of the value function is obtained and analyzed. Moreover, variational inequalities satisfied by this function are investigated. These results can be used to investigate the optimal hedging strategies and optimal exercise boundaries of the corresponding options.

scholarly journals EVOLUTION OF AMERICAN OPTION VALUE FUNCTION ON A DIVIDEND PAYING STOCK UNDER JUMP-DIFFUSION PROCESSES

2017 ◽  
Vol 2 (3) ◽  
pp. 212-221
Author(s):  
Назир Рехман ◽  
Nazir Rekhman ◽  
Закир Хуссейн ◽  
Zakir Khusseyn ◽  
Файха Али ◽  
...  
Keyword(s):  
Variational Inequalities ◽  
Value Function ◽  
Diffusion Processes ◽  
Equivalent Form ◽  
Jump Diffusion ◽  
American Option ◽  
Option Value ◽  
Jump Diffusion Processes ◽  
Hedging Strategies ◽  
The Value Function

This work is devoted to the analysis and evolution of the value function of American type options on a dividend paying stock under jump diffusion processes. An equivalent form of the value function is obtained and analyzed. Moreover, variational inequalities satisfied by this function are investigated. These results can be used to investigate the optimal hedging strategies and optimal exercise boundaries of the corresponding options.

THE VALUATION OF RUSSIAN OPTIONS FOR DOUBLE EXPONENTIAL JUMP DIFFUSION PROCESSES

2010 ◽  
Vol 27 (02) ◽  
pp. 227-242 ◽  
Author(s):  
ATSUO SUZUKI ◽  
KATSUSHIGE SAWAKI
Keyword(s):  
Value Function ◽  
Diffusion Processes ◽  
Closed Form Solution ◽  
Jump Diffusion ◽  
Form Solution ◽  
Jump Diffusion Processes ◽  
Double Exponential ◽  
Analytical Properties ◽  
Russian Option ◽  
The Value Function

In this paper, we derive closed form solution for Russian option with jumps. First, we discuss the pricing of Russian options when the stock pays dividends continuously. Secondly, we derive the value function of Russian options by solving the ordinary differential equation with some conditions (the value function is continuous and differentiable at the optimal boundary for the buyer). And we investigate properties of optimal boundaries of the buyer. Finally, some numerical results are presented to demonstrate analytical properties of the value function.

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