Regime Classification and Stock Loan Valuation

Abstract

For traditional perpetual American put options under regime-switching models with positive risk-free interest rates, optimal stopping usually can occur in any regime. Nonetheless, if the risk-free interest rates are allowed to equal zero (the interest rate may drop to zero sometimes in reality), there may exist “continuation regimes” within which optimal stopping can never occur, that is, within which stopping is never optimal. A natural problem is “regime classification,” that is, determination of all continuation regimes. In “Regime Classification and Stock Loan Valuation,” Ning Cai and Wei Zhang develop a unified, fixed point approach to solving this regime classification problem under general regime-switching exponential Levy models with any finite numbers of regimes and general Levy types. Applying this result, they also provide a unified framework for the valuation of infinite maturity stock loans under general regime-switching exponential Levy models.