Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td align="left">Statistics</td><td align="center">Rates of return for China Guodian warrants</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td align="left">Mean value</td><td align="center">−0.00025</td></tr><tr><td align="left">Maximum</td><td align="center">0.288731</td></tr><tr><td align="left">Minimum</td><td align="center">−0.15535</td></tr><tr><td align="left">Variance</td><td align="center">0.00168</td></tr><tr><td align="left">Median</td><td align="center">0.002021</td></tr><tr><td align="left">Skewness</td><td align="center">0.905533</td></tr><tr><td align="left">Kurtosis</td><td align="center">10.6741</td></tr><tr><td align="left"><svg height="11.006pt" id="M129" style="vertical-align:-2.00805pt" version="1.1" viewbox="-0.0498162 -8.99795 6.24637 11.006" width="6.24637pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M429 650H175L169 622C251 614 259 612 244 532L174 152C163 91 152 37 135 -6C109 -72 67 -101 23 -113L33 -144C45 -143 73 -134 102 -119C186 -76 229 -1 254 133L327 532C341 609 347 613 423 622L429 650Z" id="g113-75"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="452" vert-adv-y="452"></glyph.data></g></svg>-<svg height="9.04777pt" id="M130" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.99795 8.27261 9.04777" width="8.27261pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z" id="g113-67"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="601" vert-adv-y="601"></glyph.data></g></svg> statistics</td><td align="center">875.5861</td></tr><tr><td align="left">Probability</td><td align="center">0.001</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

The basic statistical characteristics of China Guodian warrants (data sources: China Tai’an database).

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tab2

Table 2

Table 2: Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion 