Document Zbl 1546.91254

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Comput. Appl. Math.</a> <a href="/?q=in%3A515599" title="Articles in this Issue">451, Article ID 116014, 15 p. (2024)</a>. </div> <div class="abstract">Summary: This study develops a closed-form solution for pricing vulnerable lookback options, which combines the Black-Scholes model for the underlying asset and a correlated jump-diffusion model for the issuer’s asset to account for default risks. Our approach relies on applying Laplace transforms to establish a closed-form solution and compute them numerically using Laplace inversion algorithms. To determine the price, we derive the joint distribution of the first passage time of a drifted Brownian motion and the value of the correlated jump-diffusion. Through numerical examples, we demonstrate the accuracy of the numerical solutions obtained through our method and the stability of the algorithm. Subsequently, we conduct a numerical analysis to understand how counterparty risk influences option prices based on our formula.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A91G20" title="MSC2020">91G20</a> </td> <td class="space"> Derivative securities (option pricing, hedging, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A60J74" title="MSC2020">60J74</a> </td> <td class="space"> Jump processes on discrete state spaces </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A44A10" title="MSC2020">44A10</a> </td> <td class="space"> Laplace transform </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Alookback+options">lookback options</a>; <a href="/?q=ut%3Avulnerable+options">vulnerable options</a>; <a href="/?q=ut%3Afirst+passage+time">first passage time</a>; <a href="/?q=ut%3Ajump-diffusion">jump-diffusion</a>; <a href="/?q=ut%3ALaplace+transforms">Laplace transforms</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1546.91254" data-ciurl="/ci/07890866" data-biburl="/bibtex/07890866.bib" data-amsurl="/amsrefs/07890866.bib" data-xmlurl="/xml/07890866.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07890866.pdf" title="Zbl 1546.91254 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.cam.2024.116014" aria-label="DOI for “Pricing vulnerable lookback options using Laplace transforms”" title="10.1016/j.cam.2024.116014">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Goldman, M. 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