Russian options with a finite time horizon

2004 ◽  
Vol 41 (2) ◽  
pp. 313-326 ◽  
Author(s):  
Erik Ekström
Keyword(s):  
Asymptotic Behavior ◽  
Free Boundary ◽  
Boundary Problem ◽  
Optimal Stopping ◽  
Finite Time ◽  
Time Horizon ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Finite Time Horizon ◽  
Russian Option

We investigate the Russian option with a finite time horizon in the standard Black–Scholes model. The value of the option is shown to be a solution of a certain parabolic free boundary problem, and the optimal stopping boundary is shown to be continuous. Moreover, the asymptotic behavior of the optimal stopping boundary near expiration is studied.

Russian options with a finite time horizon

2004 ◽  
Vol 41 (02) ◽  
pp. 313-326 ◽  
Author(s):  
Erik Ekström
Keyword(s):  
Asymptotic Behavior ◽  
Free Boundary ◽  
Boundary Problem ◽  
Optimal Stopping ◽  
Finite Time ◽  
Time Horizon ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Finite Time Horizon ◽  
Russian Option

We investigate the Russian option with a finite time horizon in the standard Black–Scholes model. The value of the option is shown to be a solution of a certain parabolic free boundary problem, and the optimal stopping boundary is shown to be continuous. Moreover, the asymptotic behavior of the optimal stopping boundary near expiration is studied.

scholarly journals On a Free Boundary Problem for American Options Under the Generalized Black–Scholes Model

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1563
Author(s):  
Jung-Kyung Lee
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
American Options ◽  
Closed Form Solution ◽  
Numerical Results ◽  
Put Options ◽  
Optimal Exercise Boundary ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Exercise Boundary

We consider the problem of pricing American options using the generalized Black–Scholes model. The generalized Black–Scholes model is a modified form of the standard Black–Scholes model with the effect of interest and consumption rates. In general, because the American option problem does not have an exact closed-form solution, some type of approximation is required. A simple numerical method for pricing American put options under the generalized Black–Scholes model is presented. The proposed method corresponds to a free boundary (also called an optimal exercise boundary) problem for a partial differential equation. We use a transformed function that has Lipschitz character near the optimal exercise boundary to determine the optimal exercise boundary. Numerical results indicating the performance of the proposed method are examined. Several numerical results are also presented that illustrate a comparison between our proposed method and others.

A Competitive Optimal Stopping Game

2017 ◽  
Vol 18 (1) ◽  
Author(s):  
Mark Whitmeyer
Keyword(s):  
Nash Equilibrium ◽  
Optimal Stopping ◽  
Finite Time ◽  
Time Horizon ◽  
Cutoff Value ◽  
Bayesian Nash Equilibrium ◽  
Stopping Game ◽  
Player Game ◽  
Finite Time Horizon

AbstractThis paper explores a multi-player game of optimal stopping over a finite time horizon. A player wins by retaining a higher value than her competitors do, from a series of independent draws. In our game, a cutoff strategy is optimal, we derive its form, and we show that there is a unique Bayesian Nash Equilibrium in symmetric cutoff strategies. We establish results concerning the cutoff value in its limit and expose techniques, in particular, use of the Budan-Fourier Theorem, that may be useful in other similar problems.

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