{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T16:00:44Z","timestamp":1790697644021,"version":"4.1.0"},"posted":{"date-parts":[[2026]]},"group-title":"SSRN","reference-count":0,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<div>\n This report describes a multi-asset pipeline we built for modeling risk and return, using a discretized Neural SDE-inspired approach. We worked with historical NIFTY 50 constituent data from 2010 to 2019. The core challenge we ran into early on is that market data is noisy, the set of assets changes over time, and expected return is much harder to estimate reliably than volatility. Because of that, we did not try to build one big model that directly predicts future returns. Instead, we split the problem into stages: first clean the data, then estimate volatility and covariance, then learn a common time-varying signal called lambda that acts as a market risk-premium proxy, and finally build an expected excess return estimate from sigma and lambda together.&nbsp;\n<\/div>\n<div>\n <br>\n<\/div>\n<div>\n The part that worked best for us is the sigma stage. On the test split, our covariance-driven sigma outperformed simple rolling-window and EWMA baselines on both correlation and error, which we think is genuine evidence of out-of-sample usefulness rather than just fitting noise. The lambda stage is more modest. It does show some connection to future market conditions out of sample, but we would not describe it as a precise return forecast. The mu stage inherits both the good and the bad from the earlier two stages: it has some regime awareness, but it is clearly the weakest part.&nbsp;\n<\/div>\n<div>\n <br>\n<\/div>\n<div>\n Overall, this project is best understood as a structured and interpretable framework for volatility and market-regime modeling. We are not claiming it is an exact market price of risk estimator. What we think it does reasonably well is show that a careful staged pipeline can produce meaningful intermediate signals, especially on the risk side, while being honest about how much harder the return side is.\n<\/div><\/jats:p>","DOI":"10.2139\/ssrn.7535838","type":"posted-content","created":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T15:07:38Z","timestamp":1790694458000},"source":"Crossref","is-referenced-by-count":0,"title":["Discretized Neural SDE for Market Price of Risk andReturn in a Multi-asset Setting"],"prefix":"10.2139","author":[{"given":"Mohd.Farzan","family":"Bhalara","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ashka","family":"Pathak","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","container-title":[],"original-title":[],"deposited":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T15:07:38Z","timestamp":1790694458000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ssrn.com\/abstract=7535838"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2139\/ssrn.7535838","relation":{},"subject":[],"published":{"date-parts":[[2026]]},"subtype":"preprint"}}