Factorization Method For Asset Pricing In Regime Switching Problems

When the profit stream of an asset depends on not only the price offundamental, but also the possible intervention expected from theauthority. The pricing problem is usually characterized by regime-switchmodel. Regime-switch problem is an adjust of traditional model; it isapplied to characterize the profit stream of an asset, which allowspossible unexpected events. In the actual investment, investors oftenchoose to terminate a contract or change a portfolio when the asset valuereach some psychological expectations (threshold). Thus,to study howshould an enterprise to operate or make decisions, such as adding a newinvestment or reduction of existing investment, choose the threadsholdfor new projects or terminate the old ones, even change a piece ofequipment, regime switch model can be used. According to differentstrategies, regime switch problem can be classified in one-sidedirreversible intervention, two-sided irreversible intervention,andstate-dependent switch policy ect. This paper is going to study thevalueation under one-sided irreversible intervention.In the study of asset pricing problems, asset price is usually calculatedby the expected present value of a stream. To calculate expected presentvalue, different methods can be used. Using strong Markov property of thefundemental and the distribution of stopping time, Francois Pascal,Morellec Erwan(2008)[17]gain a general formula. In the study of perpetualoptions, Boyarchenko Svetlana,Levendorskii Sergei(2007)[2]used Lévyexponent of the fundemental and Wiener-Hopf factorization of EPV operatorto calculate.Used the first method, Francois Pascal,Morellec Erwan(2008)[17]have gainedthe formular for asste pricing under regime switch problem. This paperwill apply the second method used in the study of perpetual options byBoyarchenko Svetlana,Levendorskii Sergei(2007)[2]to regime switchingproblems. According to the upper side and the lower side irreversibleintervention, using Wiener-Hopf factorization, the steps for calculatingthe expected present value of a stream is given, a formula for assetpricing under regime switch problem is gained. At last, we get the closedform expressions of limit situation and the lower limit situation, whichis compared with the result of the first method.