Semi-analytic valuation of stock loans with finite maturity

Lu, Xiaoping; Putri, Endah R. M.

doi:10.1016/j.cnsns.2015.03.007

Cited by 17 publications

(17 citation statements)

References 18 publications

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“…We then let the payback ∆ = 0 (no payment) in the finite maturity margin call stock loan to degenerate the margin call loan to a standard non-recourse loan, and compare our result with that of a standard non-recourse loan in [12]. As shown in Figure 3.1, our calculated dimensionless optimal exit price for ∆ = 0 agrees perfectly with that of the standard non-recourse loan.…”

Section: Methods Validationsupporting

confidence: 72%

“…It makes financial sense, as a margin call is supposed to provide more security for the lender; higher payback provides lower margin call value to the borrower. A margin call stock loan values less than a non-recourse loan so it should be cheaper to enter a margin call contract [12]. Figures 3.3 (a) and 3.3(b) show the variation of the optimal exit prices for different loan interest rate γ with all other parameters fixed.…”

Section: Margin Call Stock Loansmentioning

confidence: 99%

“…Lauko and Sevcovic [11] pointed out that the method in [17] is particularly suitable for long term American option valuation in a comparative study of numerical and analytical approximation methods of the early exercise boundary of American puts. Since a stock loan usually has a longer life time than ordinary options, the approximation method is also proved suitable in a stock loan evaluation [12]. Therefore, the approach in [13] and [17] will form the basis for the solution procedure in this study.…”

Section: Introductionmentioning

confidence: 99%

“…The margin call phase resembles an American downand-out call with rebate and the non-recourse phase resembles a vanilla American call, both with negative interest rate and time dependent strike. We will concentrate on the margin call phase in this work, the evaluation of non-recourse stock loans is presented by the authors in [12].…”

Section: Introductionmentioning

confidence: 99%

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Finite maturity margin call stock loans

Putri

2016

Operations Research Letters

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Section: Methods Validationsupporting

confidence: 72%

Section: Margin Call Stock Loansmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Finite maturity margin call stock loans

Putri

2016

Operations Research Letters

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“…For example, Dai and Xu [4] analysed stock loans in four different dividend distribution cases and calculated the prices using the binomial tree method. Lu and Putri [5] also considered the pricing of stock loans in the four divided distribution cases by using the Laplace transform method. For the valuation of stock loans under more complicated models, Pascucci et al [6] formulated the pricing of stock loans with accumulative dividends as an obstacle problem.…”

Section: Introductionmentioning

confidence: 99%

Stock loan valuation under a stochastic interest rate model

Chen

Zhu

2015

Computers & Mathematics with Applications

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a b s t r a c tStock loans are loans collateralized by stocks. They are modern financial products designed for investors with large equity positions. Mathematically, stock loans can be regarded as American call options with a time-dependent strike price. This study is the first in the literature that considers the valuation of stock loans in a stochastic interest rate framework. Based on portfolio analysis, a partial differential equation (PDE) governing the value of stock loans is derived. A set of appropriate boundary conditions, particularly in the interest rate direction, are also proposed to close the pricing system. A sound justification is provided for the proposed boundary conditions mathematically as well as financially. To solve the proposed nonlinear PDE system, a predictor-corrector finite difference method is adopted. Moreover, an alternating direction implicit (ADI) method is used to improve the computational efficiency. Numerical results suggest that the current method is reliable and the stochastic interest rate leads to a higher optimal exercise price of the stock loan in comparison with that calculated from the Black-Scholes model.

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Stabilization of a stock‐loan valuation PDE process using differential flatness theory

Rigatos

Siano

Loia

et al. 2019

Asian Journal of Control

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The article proposes flatness-based control for stabilization of a stock-loan valuation process that is described by a partial differential equation. By applying semi-discretization and the finite differences method, the state-space model of the stock loan has been obtained. It has been proven that the individual rows of this state-space model are nonlinear ODEs which can be viewed as differentially flat subsystems. For the local subsystems, into which the stock-loan PDE is decomposed, it becomes possible to apply boundary feedback control. The controller design proceeds by showing that the state-space model of the stock loan PDE stands for a differentially flat system. Next, for each subsystem which is related to a nonlinear ODE, a virtual control input is computed, that can invert the subsystem's dynamics and can eliminate the subsystem's tracking error. From the last row of the state-space description, the control input (boundary condition) that is actually applied to the stock loan PDE system is found. This control input contains recursively all virtual control inputs which were computed for the individual ODE subsystems associated with the previous rows of the state-space description. Thus, by tracing the rows of the state-space model backwards, at each iteration of the control algorithm, one can finally obtain the control input that should be applied to the stock loan PDE system so as to assure that all its state variables will converge to the desirable setpoints.By showing the feasibility of such a control method it is also proven that through selected modification of the PDE boundary conditions the value of the stock loan can be made to converge and stabilize at specific reference values.

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Semi-analytic valuation of stock loans with finite maturity

Cited by 17 publications

References 18 publications

Finite maturity margin call stock loans

Finite maturity margin call stock loans

Stock loan valuation under a stochastic interest rate model

Stabilization of a stock‐loan valuation PDE process using differential flatness theory

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