Geodesic
Asymptotic analysis for stock loans near maturity
Filomat, Tome 37 (2023) no. 7, p. 2105

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DOI

In this paper, we derive the asymptotic expressions of the scaled value function and the optimal redemption boundary of stock loan with dividend-paying near maturity. Using the equation satisfied by the derivative of the value function at the exercise boundary, we set up the asymptotic expression for the boundary. When the risk-free rate r is smaller than the loan rate β, i.e., r β, the boundary tends to KeβT 0 in parabolic-logarithm form, this case is the main result. For the case r ≥ β, the corresponding problem returns back to a usual American call option with interest-free rate r − β and the existing results can be utilized to make proper adjustments for the stock loan. The matched expansion for the value function is performed with a small parameter. Numerical examples are provided to demonstrate the effectiveness of the proposed method.
DOI : 10.2298/FIL2307105X
Classification : 35K20, 91G20, 91G80
Keywords: stock loan, risk-free rate, dividend, loan rate, Black-Scholes equation, free boundary 
Yongqing Xu. Asymptotic analysis for stock loans near maturity. Filomat, Tome 37 (2023) no. 7, p. 2105 . doi: 10.2298/FIL2307105X
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     title = {Asymptotic analysis for stock loans near maturity},
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     doi = {10.2298/FIL2307105X},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2307105X/}
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