Pricing of Fixed-Strike Lookback Options on Assets with Default Risk

<table class="fixed-width table-group" id="tab3"><tr><td><table class="table"><colgroup><col style="width:14.47em"/><col style="width:12.71em"/><col style="width:9.90em"/><col style="width:7.42em"/></colgroup><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left"><svg height="8.8423pt" id="M176" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 9.35121 8.8423" width="9.35121pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 278 116H276C239 278 197 500 186 567C180 604 185 613 226 619L252 623L260 650H24L17 623C78 617 92 613 108 533L216 -11H247C365 200 515 462 560 529C616 612 624 615 689 623L697 650Z"></path></g></svg>(Market value of option writer)</td><td class="align_center"> Monte-Carlo simulation</td><td class="align_center"> Closed-form solution</td><td class="align_center"> Relative error 1</td></tr><tr><td class="align_left" colspan="4"><hr/></td></tr><tr><td class="align_left">90</td><td class="align_center"> 14.0193</td><td class="align_center"> 14.1606</td><td class="align_center"> 0.00997</td></tr><tr><td class="align_left">100</td><td class="align_center"> 15.9428</td><td class="align_center"> 16.0846</td><td class="align_center"> 0.00881</td></tr><tr><td class="align_left">110</td><td class="align_center"> 17.0710</td><td class="align_center"> 17.2383</td><td class="align_center"> 0.00970</td></tr><tr><td class="align_left">120</td><td class="align_center"> 17.6482</td><td class="align_center"> 17.8269</td><td class="align_center"> 0.01002</td></tr><tr><td class="align_left" colspan="4"><hr/></td></tr><tr><td class="align_left"><svg height="8.8423pt" id="M177" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 9.35121 8.8423" width="9.35121pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 278 116H276C239 278 197 500 186 567C180 604 185 613 226 619L252 623L260 650H24L17 623C78 617 92 613 108 533L216 -11H247C365 200 515 462 560 529C616 612 624 615 689 623L697 650Z"></path></g></svg>(Market value of option writer)</td><td class="align_center"> Numerical Solution by FDM</td><td class="align_center"> Closed-form solution</td><td class="align_center"> Relative error 2</td></tr><tr><td class="align_left" colspan="4"><hr/></td></tr><tr><td class="align_left">90</td><td class="align_center"> 14.2143</td><td class="align_center"> 14.1606</td><td class="align_center"> 0.00379</td></tr><tr><td class="align_left">100</td><td class="align_center"> 16.1701</td><td class="align_center"> 16.0846</td><td class="align_center"> 0.00531</td></tr><tr><td class="align_left">110</td><td class="align_center"> 17.0127</td><td class="align_center"> 17.2383</td><td class="align_center"> 0.01309</td></tr><tr><td class="align_left">120</td><td class="align_center"> 17.4634</td><td class="align_center"> 17.8269</td><td class="align_center"> 0.02039</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Change in the relative errors for the Monte-Carlo simulation and the numerical solution by Finite Difference Method (FDM) against closed-form solution of VFSLCO with regard to the market value of the option’s writer. The parameter values chosen are <span class="nowrap"><svg height="9.01194pt" id="M166" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.96212 29.5984 9.01194" width="29.5984pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.917,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.18,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g></svg>,</span> <span 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Mathematical Problems in Engineering

Pricing of Fixed-Strike Lookback Options on Assets with Default Risk

Table 3