Stock loans are business contracts between borrowers and lenders in which the borroweruses shares of stock as collateral for the loan.Since the value of the collateral is subject to wide andfrequent price swings,valui...Stock loans are business contracts between borrowers and lenders in which the borroweruses shares of stock as collateral for the loan.Since the value of the collateral is subject to wide andfrequent price swings,valuing such a transaction behaves more like an option pricing problem thana debt valuation problem.This paper will list,prove,and analyze formulas for stock loan valuationwith finite horizon under various stock models,including classical geometric Brownian motion,meanreverting,and two-state regime-switching with both mean-reverting and geometric Brownian motionstates.Numerical examples are reported to illustrate the results.展开更多
In recent years the use of Markov chain models to model stock price movement has received increased attention among researchers.Markov chain models combine the discrete movements of a binomial tree model while retaini...In recent years the use of Markov chain models to model stock price movement has received increased attention among researchers.Markov chain models combine the discrete movements of a binomial tree model while retaining the Markovian properties of Brownian motion,thus allowing the best properties of both of these models.In this paper,the authors consider a Markov chain model in which the underlying market is solely determined by a two-state Markov chain.Such a Markov chain model is strikingly simple and yet appears capable of capturing various market movements.By proper selection of parameters,the Markov chain model can produce sample paths that are very similar to.or very distinct from a classical Brownian motion,as the authors demonstrate in this paper.This paper studies the stock loan valuation,or the value of a loan in which a risky share of stock is used as collateral,under such a model.Dynamic programming equations in terms of variational inequalities are used to capture the dynamics of the problem.These equations are solved in closed-form.Explicit optimal solutions are obtained.Numerical examples are also reported to illustrate the results.展开更多
文摘Stock loans are business contracts between borrowers and lenders in which the borroweruses shares of stock as collateral for the loan.Since the value of the collateral is subject to wide andfrequent price swings,valuing such a transaction behaves more like an option pricing problem thana debt valuation problem.This paper will list,prove,and analyze formulas for stock loan valuationwith finite horizon under various stock models,including classical geometric Brownian motion,meanreverting,and two-state regime-switching with both mean-reverting and geometric Brownian motionstates.Numerical examples are reported to illustrate the results.
基金supported in part by the Simons Foundation(235179 to ZHANG Qing)
文摘In recent years the use of Markov chain models to model stock price movement has received increased attention among researchers.Markov chain models combine the discrete movements of a binomial tree model while retaining the Markovian properties of Brownian motion,thus allowing the best properties of both of these models.In this paper,the authors consider a Markov chain model in which the underlying market is solely determined by a two-state Markov chain.Such a Markov chain model is strikingly simple and yet appears capable of capturing various market movements.By proper selection of parameters,the Markov chain model can produce sample paths that are very similar to.or very distinct from a classical Brownian motion,as the authors demonstrate in this paper.This paper studies the stock loan valuation,or the value of a loan in which a risky share of stock is used as collateral,under such a model.Dynamic programming equations in terms of variational inequalities are used to capture the dynamics of the problem.These equations are solved in closed-form.Explicit optimal solutions are obtained.Numerical examples are also reported to illustrate the results.
