Document Zbl 1466.91332

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Finance</a> <a href="/?q=in%3A463936" title="Articles in this Issue">21, No. 3, 461-480 (2021)</a>. </div> <div class="abstract">Summary: In this paper, we propose a general valuation framework for option pricing problems related to skew diffusions based on a continuous-time Markov chain approximation to the underlying stochastic process. We obtain an explicit closed-form approximation of the transition density of a general skew diffusion process, which facilitates the unified valuation of various financial contracts written on assets with natural boundary behavior, e.g. in the foreign exchange market with target zones, and equity markets with psychological barriers. Applications include valuation of European call and put options, barrier and Bermudan options, and zero-coupon bonds. Motivated by the presence of psychological barriers in the market volatility, we also propose a novel ‘skew stochastic volatility’ model, in which the latent stochastic variance follows a skew diffusion process. Numerical results demonstrate that our approach is accurate and efficient, and recovers various benchmark results in the literature in a unified fashion.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7353690">Cited in <strong>10</strong> Documents</a></div></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%3A60J28" title="MSC2020">60J28</a> </td> <td class="space"> Applications of continuous-time Markov processes on discrete state spaces </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Askew+diffusion">skew diffusion</a>; <a href="/?q=ut%3Alocal+time">local time</a>; <a href="/?q=ut%3Acontinuous-time+Markov+chain">continuous-time Markov chain</a>; <a href="/?q=ut%3Aoption+pricing">option pricing</a>; <a href="/?q=ut%3Atarget+zone">target zone</a>; <a href="/?q=ut%3Apsychological+barriers">psychological barriers</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 1466.91332" data-ciurl="/ci/07353690" data-biburl="/bibtex/07353690.bib" data-amsurl="/amsrefs/07353690.bib" data-xmlurl="/xml/07353690.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07353690.pdf" title="Zbl 1466.91332 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/10.1080/14697688.2020.1781235" aria-label="DOI for “A Markov chain approximation scheme for option pricing under skew diffusions”" title="10.1080/14697688.2020.1781235">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">Appuhamillage, T. and Sheldon, D., First passage time of skew Brownian motion. <span class="zbmathjax-textit">J. 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