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This paper will focus on pricing options in marketing with two basic assets with risk and one basic asset without risk. In so doing, the Black-Scholes model and the European options which is applicable at the due date were used. By investigating the European option to find the proper price, it is necessary to solve an equation with partial derivati...
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Context 1
... the volatility of the first and second assets are shown by 1 2 , σ σ and the ρ is the correlation coefficient between the prices of the two underlying assets and r is interest rate, then ( ) , , u x y T is the this contract price in the following equation which is called the two dimensional Black-Scholes equation. 2 2 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 . To use numerical methods, a limited range will be considered. ...Context 2
... simplify the computations, the discrete operator L is defined as follows [3]. ) 2 2 2 2 1, , 1, , 1 , , 1 1 2 2 2 1, 1 , 1 1, , 1 2 1, 1, , 1 , 1 , 2 2 , 2 2 . 2 2 n n n n n n i j i j i j i j i j i j n ij n n n n i ...Context 3
... other words, we implicitly estimate the derivation in relation to y and explicitly in relation to x. Therefore, we have 1 1 1 1 1 1 2 2 2 2 2 2 , , 1, , 1, , 1 , , 1 2 2 1 2 2 2 1 1 1 1 2 2 2 is defined which is a three diagonal set. ...Context 6
... this example, the errors of both ADI and LOD methods with different time and location step length are presented in Table 1 and Table 2. Figure 2. The income function of option of two cash assets or none. ...Context 7
... shown in Table 1, the ADI shows better convergence than the LOD method with relatively large space step sizes. However, with smaller space step size (equivalently large temporal step size), convergence the method ADI shows the results which have big error while the method LOD make convergent results. ...