scholarly journals On perpetual American options in a multidimensional Black–Scholes model

Stochastics ◽  
2021 ◽  
pp. 1-22
Author(s):  
Andrzej Rozkosz
Keyword(s):  
American Options ◽  
Black Scholes Model ◽  
Black Scholes

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.

scholarly journals Shortfall Risk Approximations for American Options in the Multidimensional Black-Scholes Model

2010 ◽  
Vol 47 (4) ◽  
pp. 997-1012
Author(s):  
Yan Dolinsky
Keyword(s):  
Weak Convergence ◽  
American Options ◽  
Shortfall Risk ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Path Dependent ◽  
Weak Convergence Approach

We show that shortfall risks of American options in a sequence of multinomial approximations of the multidimensional Black-Scholes (BS) market converge to the corresponding quantities for similar American options in the multidimensional BS market with path-dependent payoffs. In comparison to previous papers we consider the multiassets case for which we use the weak convergence approach.

Pricing European and American Options by SPH Method

2019 ◽  
Vol 17 (08) ◽  
pp. 1950043
Author(s):  
B. Achchab ◽  
A. Cheikh Maloum ◽  
A. Qadi El Idrissi
Keyword(s):  
Differential Equation ◽  
American Options ◽  
Time Variable ◽  
Sph Method ◽  
Numerical Tests ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Smoothed Particle ◽  
The Finite Difference Method ◽  
Smoothed Particle Hydrodynamic

In this paper, the meshless smoothed particle hydrodynamic (SPH) method is applied for solving the Black–Scholes model for European and American options, which are governed by a generalized Black–Scholes partial differential equation. We use the [Formula: see text]-method and SPH for discretizing the governing equation in time variable and option pricing, respectively. To validate our SPH method, we compare it with the analytical solution and also the finite difference method. The numerical tests demonstrate the accuracy and robustness of our method.

scholarly journals Shortfall Risk Approximations for American Options in the Multidimensional Black-Scholes Model

2010 ◽  
Vol 47 (04) ◽  
pp. 997-1012
Author(s):  
Yan Dolinsky
Keyword(s):  
Weak Convergence ◽  
American Options ◽  
Shortfall Risk ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Path Dependent ◽  
Weak Convergence Approach

We show that shortfall risks of American options in a sequence of multinomial approximations of the multidimensional Black-Scholes (BS) market converge to the corresponding quantities for similar American options in the multidimensional BS market with path-dependent payoffs. In comparison to previous papers we consider the multiassets case for which we use the weak convergence approach.

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