Abstract
The pricing of the two-asset double barrier option is modeled as an initial-boundary value problem of the two-dimensional Black-Scholes partial differential equation. We use the hybrid finite different method to solve the problem. The hybrid method is a combination of the Laplace transform and a finite difference method. It is more efficient than a traditional finite difference method to obtain a solution without a step-by-step process. The method is implemented on a computer. Two numerical examples are calculated to verify the performance of the hybrid method. In our numerical examples, the convergence rate of the method is approximately two. We conclude that the method is efficient for pricing two-asset barrier options.
Highlights
Pricing financial derivatives is important in financial engineering
In order to solve the homogeneous heat equation [2,3,4], the method we introduced is first applied in pricing the two-asset double barrier option
Pricing financial derivatives is a mathematical problem in financial engineering
Summary
Pricing financial derivatives is important in financial engineering. Following Black-Scholes arguments [1], pricing a two-asset double barrier option is an initial-boundary value problem of the Black-Scholes partial differential equation (PDE). We use the hybrid finite difference method to calculate the price of two-asset double barrier option. In order to solve the homogeneous heat equation [2,3,4], the method we introduced is first applied in pricing the two-asset double barrier option. Some methods have solved the one-dimensional Black-Scholes PDE directly, for example, in [8]. We introduce the hybrid finite difference method to price the two-asset double barrier option.
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