Valuing options under regime switching environment

Abstract

In this dissertation, we study for valuing options where its underlying assets are affected by stochastically changing market environments of economic, political factors and business cycle. First we find a closed-form formula of a time switch option whose payoff is related to the number of days the underlying asset prices has spent above a barrier, using a Markov regime-switching for the volatility. And we apply it to the valuation of other qualitative options such as corridor options and options in foreign exchange markets. Second we consider the problem of pricing a European-style multivariate contingent claims whose payoff function is dependent on multiple underlying assets with stochastic volatility. Finally we suggest a lattice method for valuing options which have two correlated underlying assets with stochastic volatility. A lattice method can be used in cases of absence of closed-form solution and American-style options.