This paper explores different covariance matrix estimators in application to geometric Brownian motion. Particular interest is given to shrinkage estimation methods. In collaboration with Söderberg & Partners risk management team, the goal is to find an estimation that performs well in low-data scenarios and is robust against erroneous model assumptions, particularly the Gaussian assumption of the stock price distribution. Estimations are compared by two criteria: Frobenius norm distance between the estimate and the true covariance matrix, and the condition number of the estimate. By considering four estimates — the sample covariance matrix, Ledoit-Wolf, Tyler M-estimator, and a novel Tyler-Ledoit-Wolf (TLW) estimator — this paper concludes that the TLW estimator performs best when considering the two criteria.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kth-348639 |
| Date | January 2024 |
| Creators | Spector, Erik |
| Publisher | KTH, Skolan för teknikvetenskap (SCI) |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | TRITA-SCI-GRU ; 2024:248 |
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