{"id":2290,"date":"2025-11-17T12:27:46","date_gmt":"2025-11-17T12:27:46","guid":{"rendered":"https:\/\/blogs.mathworks.com\/finance\/?p=2290"},"modified":"2025-11-18T11:04:47","modified_gmt":"2025-11-18T11:04:47","slug":"pricing-special-purpose-vehicles-with-physics%e2%80%91informed-neural-networks-at-nasdaq-private-market","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/finance\/2025\/11\/17\/pricing-special-purpose-vehicles-with-physics%e2%80%91informed-neural-networks-at-nasdaq-private-market\/","title":{"rendered":"Pricing Special Purpose Vehicles with Physics\u2011Informed Neural Networks at Nasdaq Private Market"},"content":{"rendered":"<h1><strong>Summary<\/strong><\/h1>\n<p>Nasdaq Private Market (NPM) used MATLAB\u00ae to prototype and scale physics\u2011informed neural networks (PINNs) that price Special Purpose Vehicles (SPVs) with embedded carried interest and uncertain exit timing.<\/p>\n<p>&nbsp;<\/p>\n<blockquote>\n<div style=\"border-left: 5px solid #ccc;padding-left: 20px;margin: 20px 0;font-style: italic;font-size: 0.9em;color: #333\">&#8220;Deep Learning Toolbox\u2122 allowed me to prototype quickly, like for example using Deep Network Designer, and very few moving parts. In other words, I could spin out my proof of concept very fast.&#8221;<br \/>\n<cite style=\"font-style: normal;font-weight: bold;color: #555\">\u2014 Chetan Jadhav, Senior Data Scientist, Nasdaq Private Markets<\/cite><\/div>\n<\/blockquote>\n<p>&nbsp;<\/p>\n<p style=\"font-size: 1.2em;font-weight: bold\">Watch the video: <a href=\"https:\/\/www.mathworks.com\/videos\/special-purpose-vehicle-spv-pricing-using-physics-informed-neural-networks-1760427215170.html?s_eid=OIT_1763376373\" target=\"_blank\" rel=\"noopener\"><em>Special Purpose Vehicle (SPV) Pricing Using Physics-Informed Neural Networks<\/em><\/a><\/p>\n<p>&nbsp;<\/p>\n<h1><strong>Key Outcomes<\/strong><\/h1>\n<ul>\n<li data-start=\"3800\" data-end=\"4013\">\n<p data-start=\"3802\" data-end=\"4013\"><strong data-start=\"3802\" data-end=\"3843\">Pricing with domain knowledge and AI:<\/strong> NPM prices SPVs by treating carried interest as an embedded option and modeling uncertain exit timing. The models include carry and fees for structure\u2011aware valuation.<\/p>\n<\/li>\n<li data-start=\"4014\" data-end=\"4318\">\n<p data-start=\"4016\" data-end=\"4318\"><strong data-start=\"4016\" data-end=\"4054\">Prototyping and scaling in MATLAB:<\/strong> The team trained PINNs with Deep Learning Toolbox\u2122 and Parallel Computing Toolbox\u2122, distributing Monte Carlo simulations across GPUs on AWS. On a four\u2011GPU instance, they report about an 800\u00d7 speedup versus a laptop, enabling rapid iteration.<\/p>\n<\/li>\n<li data-start=\"4319\" data-end=\"4536\">\n<p data-start=\"4321\" data-end=\"4536\"><strong data-start=\"4321\" data-end=\"4358\">Accuracy and structure detection:<\/strong> PINNs tracked SPV price moves and surfaced structural pricing patterns in private trades. The networks aligned with theory and showed less overfitting on synthetic validation.<\/p>\n<\/li>\n<li data-start=\"4537\" data-end=\"4681\">\n<p data-start=\"4539\" data-end=\"4681\"><strong data-start=\"4539\" data-end=\"4567\">Technical collaboration:<\/strong> NPM worked with MathWorks Consulting Services to refine the modeling workflow and optimize deployment on AWS.<\/p>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<blockquote>\n<div style=\"border-left: 5px solid #ccc;padding-left: 20px;margin: 20px 0;font-style: italic;font-size: 0.9em;color: #333\">\u201cThey [MathWorks technical support] even answer your model-related questions\u201d<br \/>\n<cite style=\"font-style: normal;font-weight: bold;color: #555\">\u2014 Chetan Jadhav<\/cite><\/div>\n<\/blockquote>\n<h1><strong>Engineering the SPV Pricing Workflow<\/strong><\/h1>\n<p data-start=\"4818\" data-end=\"5255\">SPVs are hard to value because of illiquidity, opaque prices, and embedded carry. Rather than fold carry into an ad\u2011hoc discount, NPM modeled it as a short call embedded in the SPV. Liquidity events (for example, IPOs or acquisitions) are random, which makes maturity stochastic and decouples valuation from a fixed maturity date. Daily price and volatility signals from Tape D\u00ae anchored parameters for simulation and validation.<\/p>\n<h1><strong>Why Physics-Informed Neural Networks<\/strong><\/h1>\n<p>PINNs combine machine learning with the rigor of differential equations. Instead of only fitting data, they learn to satisfy the governing Black\u2013Scholes\u2011type PDE with liquidity risk, carry fees, and other embedded terms. This lets the model work with thin or synthetic datasets by enforcing known relationships in the loss function. For NPM, that meant training on synthetic Monte Carlo samples when real SPV trade data was limited\u2014while keeping financial realism and interpretability.<\/p>\n<blockquote>\n<div style=\"border-left: 5px solid #ccc;padding-left: 20px;margin: 20px 0;font-style: italic;font-size: 0.9em;color: #333\">\u201cPINNs are a great fit for SPV pricing &#8230; They don\u2019t just fit the data \u2014 they learn the solution of the equation.\u201d<br \/>\n<cite style=\"font-style: normal;font-weight: bold;color: #555\">\u2014 Chetan Jadhav<\/cite><\/div>\n<\/blockquote>\n<p>This design allows PINNs to handle thin or synthetic datasets by enforcing known relationships through their loss function. For NASDAQ Private Markets, this meant the models could be trained entirely on synthetic Monte Carlo samples when real SPV trade data was limited, while still preserving financial realism and interpretability.<\/p>\n<p>&nbsp;<\/p>\n<h1><strong>Model Development and Training<\/strong><\/h1>\n<p>The team built a custom 10\u2011layer network in the Deep Network Designer app, using swish activations and tuned initialization. Training combined loss terms for PDE residuals, boundary conditions, and Monte Carlo\u2011based components to improve stability and accuracy. Focused sampling near payoff kinks improved precision.<\/p>\n<p>&nbsp;<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-2358 size-full\" src=\"http:\/\/blogs.mathworks.com\/finance\/files\/2025\/11\/Slide-NEW.png\" alt=\"\" width=\"1661\" height=\"907\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>With Parallel Computing Toolbox\u2122, they distributed Monte Carlo simulation across multiple GPUs on AWS, achieving the reported ~800\u00d7 acceleration versus single\u2011machine runs. They streamlined training and deployment with MATLAB Compiler SDK\u2122 and Docker\u00ae containers on AWS App Runner for reproducible, cloud\u2011based inference.<\/p>\n<h1><strong>Results and Insights<\/strong><\/h1>\n<p data-start=\"6642\" data-end=\"7093\">Once trained, the PINNs tracked SPV price movements and revealed <strong data-start=\"6707\" data-end=\"6731\">consistent discounts<\/strong> in certain private trades relative to model\u2011based fair values. This pattern suggests that some carry terms may be underpriced\u2014useful insight for investors and issuers. Compared with ensemble regression on limited real data, the PINNs were closer to theoretical ground truth and generalized better to synthetic validation sets, indicating lower overfitting risk.<\/p>\n<h1><strong>Scaling and Operational Impact<\/strong><\/h1>\n<p data-start=\"7130\" data-end=\"7379\">Using MATLAB <strong data-start=\"7143\" data-end=\"7153\">on AWS<\/strong>, NPM built an end\u2011to\u2011end workflow\u2014from prototyping to cloud deployment\u2014without heavy rewrites. Hybrid CPU\/GPU scaling let the team use compute efficiently, and Docker made inference portable across development and production.<\/p>\n<blockquote>\n<div style=\"border-left: 5px solid #ccc;padding-left: 20px;margin: 20px 0;font-style: italic;font-size: 0.9em;color: #333\">\u201cThis approach would not be possible without [our daily pricing and volatility product]. \u2026 Some of the recent improvements in this product were developed in collaboration with the MathWorks consulting team.&#8221;<br \/>\n<cite style=\"font-style: normal;font-weight: bold;color: #555\">\u2014 Chetan Jadhav<\/cite><\/div>\n<\/blockquote>\n<h1><strong data-start=\"7558\" data-end=\"7570\">Outcome<\/strong><\/h1>\n<p>A consistent, scalable pricing workflow that helps investors, sellers, and intermediaries compare SPVs more confidently.<\/p>\n<p>&nbsp;<\/p>\n<h1><strong>Learn More<\/strong><\/h1>\n<ul>\n<li><a href=\"https:\/\/www.mathworks.com\/discovery\/physics-informed-neural-networks.html\">Physics-Informed Neural Networks: An Introduction<\/a><\/li>\n<li><a href=\"https:\/\/www.mathworks.com\/discovery\/financial-engineering.html\">Financial Engineering: Models, Methods, Applications<\/a><\/li>\n<li><a href=\"https:\/\/www.mathworks.com\/discovery\/market-risk.html\">Quantitative Approaches to Market Risk<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<div class=\"overview-image\"><img decoding=\"async\"  class=\"img-responsive\" src=\"http:\/\/blogs.mathworks.com\/finance\/files\/2025\/11\/Slide-NEW.png\" onError=\"this.style.display ='none';\" \/><\/div>\n<p>Summary<br \/>\nNasdaq Private Market (NPM) used MATLAB\u00ae to prototype and scale physics\u2011informed neural networks (PINNs) that price Special Purpose Vehicles (SPVs) with embedded carried interest and&#8230; <a class=\"read-more\" href=\"https:\/\/blogs.mathworks.com\/finance\/2025\/11\/17\/pricing-special-purpose-vehicles-with-physics%e2%80%91informed-neural-networks-at-nasdaq-private-market\/\">read more >><\/a><\/p>\n","protected":false},"author":233,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[10,22,31,37,25,19,34],"tags":[],"_links":{"self":[{"href":"https:\/\/blogs.mathworks.com\/finance\/wp-json\/wp\/v2\/posts\/2290"}],"collection":[{"href":"https:\/\/blogs.mathworks.com\/finance\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.mathworks.com\/finance\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/finance\/wp-json\/wp\/v2\/users\/233"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/finance\/wp-json\/wp\/v2\/comments?post=2290"}],"version-history":[{"count":69,"href":"https:\/\/blogs.mathworks.com\/finance\/wp-json\/wp\/v2\/posts\/2290\/revisions"}],"predecessor-version":[{"id":2571,"href":"https:\/\/blogs.mathworks.com\/finance\/wp-json\/wp\/v2\/posts\/2290\/revisions\/2571"}],"wp:attachment":[{"href":"https:\/\/blogs.mathworks.com\/finance\/wp-json\/wp\/v2\/media?parent=2290"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/finance\/wp-json\/wp\/v2\/categories?post=2290"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/finance\/wp-json\/wp\/v2\/tags?post=2290"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}