An Analysis of Asymptotic Properties and Error Control under the Exponential Jump-Diffusion Model for American Option Pricing

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/jam/volume-2021/1049907/figures/1049907.fig.005a.svgz" name="1049907.fig.005a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Equilibrium price option under B&amp;S <svg height="15.7711pt" id="M232" style="vertical-align:-3.997pt" version="1.1" viewbox="-0.0498162 -11.7741 68.7377 15.7711" width="68.7377pt" 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="M715 650H476L470 622C550 619 562 610 562 570C562 536 553 481 535 384L523 321C485 121 408 37 283 37C178 37 99 109 134 297L178 532C193 612 199 616 278 622L284 650H29L23 622C105 616 109 609 94 532L48 291C23 160 51 83 98 40C143 -1 202 -16 260 -16C321 -16 387 3 439 49C509 111 542 204 563 312L577 384C595 479 608 533 619 569C629 603 637 620 709 622L715 650Z"></path></g><g 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<div>Asymptotic convergence of the least square algorithm <svg height="8.68572pt" id="M231" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 12.9526 8.68572" width="12.9526pt" 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="M962 650H795L470 145L347 650H176L170 622C268 613 275 606 244 503L190 322C150 188 132 126 118 91C102 50 80 33 18 28L12 0H245L251 28C175 35 170 48 174 93C177 128 191 180 220 284L292 542H294C331 392 383 150 409 4H432L774 555H776L714 137C700 40 694 34 612 28L606 0H868L874 28C793 34 784 37 797 137L849 533C859 612 863 616 956 622L962 650Z"></path></g></svg> from 100 to 10000. Confidence level in order of 95% (the estimated value of the American option in blue, upper bound in red, and lower bound in green).</div>

Journal of Applied Mathematics

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Figure 5

Figure 5: An Analysis of Asymptotic Properties and Error Control under the Exponential Jump-Diffusion Model for American Option Pricing 