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Stock loan valuation under a regime-switching model with mean-reverting and finite maturity

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Abstract

Stock loans are business contracts between borrowers and lenders in which the borrower uses shares of stock as collateral for the loan. Since the value of the collateral is subject to wide and frequent price swings, valuing such a transaction behaves more like an option pricing problem than a debt valuation problem. This paper will list, prove, and analyze formulas for stock loan valuation with finite horizon under various stock models, including classical geometric Brownian motion, mean-reverting, and two-state regime-switching with both mean-reverting and geometric Brownian motion states. Numerical examples are reported to illustrate the results.

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Authors and Affiliations

  1. Department of Mathematics, University of Georgia, Athens, GA, 30602, USA

    David Prager & Qing Zhang

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  1. David Prager
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  2. Qing Zhang
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Correspondence to David Prager.

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Prager, D., Zhang, Q. Stock loan valuation under a regime-switching model with mean-reverting and finite maturity. J Syst Sci Complex 23, 572–583 (2010). https://doi.org/10.1007/s11424-010-0146-7

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  • DOI: https://doi.org/10.1007/s11424-010-0146-7

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