Statistical Behavior of a Financial Model by Lattice Fractal Sierpinski Carpet Percolation

<table>(a) The plots of modified <svg height="10.9125" id="M184" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 27.2875 10.9125" width="27.2875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑅</tspan>
<tspan style="font-size: 12.50px; " x="9.2522202" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="12.728054" y="0">𝑆</tspan>
</text>
</g>
</g>
</svg> statistics and the fluctuation of exponent <svg height="10.325" id="M185" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 15.175 10.325" width="15.175" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐻</tspan>
</text>
</g>
</g>
</svg> for the price model. (b) The corresponding plots for the actual data from Hang Seng Index.</table>

Journal of Applied Mathematics

fig4

Figure 4

Figure 4: Statistical Behavior of a Financial Model by Lattice Fractal Sierpinski Carpet Percolation 