Abstract
This paper presents an explicit finite-difference method for nonlinear partial differential equation appearing as a transformed Black-Scholes equation for American put option under logarithmic front fixing transformation. Numerical analysis of the method is provided. The method preserves positivity and monotonicity of the numerical solution. Consistency and stability properties of the scheme are studied. Explicit calculations avoid iterative algorithms for solving nonlinear systems. Theoretical results are confirmed by numerical experiments. Comparison with other approaches shows that the proposed method is accurate and competitive.
Highlights
American options are contracts allowing the holder the right to sell an asset at a certain price at any time until a prespecified future date
As the best model can be wasted with a disregarded numerical analysis, in this paper, we focus on the numerical issues of explicit finite difference scheme for American put option problem after using the fixed domain transformation used in [20]
We compare explicit front fixing method (FF) with h1 = 0.001 and h2 = 0.002 and μ = 5 for American put with other numerical methods shown in [15] in Table 4 for the following problem parameters: r = 0.05, σ = 0.2, T = 3, (61)
Summary
American options are contracts allowing the holder the right to sell (buy) an asset at a certain price at any time until a prespecified future date. The American option pricing problem can be posed either as a linear complementarity problem (LCP) or a free boundary value problem. This complexity is reduced by transforming the problem into a new nonlinear partial differential equation where the free boundary appears as a new variable of the PDE problem This technique which originated in physics problems is the so called front fixing method based on Landau transform [18] to fix the optimal exercise boundary on a vertical axis. As the best model can be wasted with a disregarded numerical analysis, in this paper, we focus on the numerical issues of explicit finite difference scheme for American put option problem after using the fixed domain transformation used in [20].
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