Browsing by Author "Elliott, Robert James"

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    Pricing Options in a Finite State Markov Chain Market
    (2015-01-06) Ramarimbahoaka, Dimbinirina; Elliott, Robert James; Swishchuk, Anatoliy
    We consider a finite state Markov chain which models uncertainties in a financial market. A stochastic discount function is considered and prices of perpetual American options and optimal exercise times are initially investigated using a stationary variational inequality. Our next topic uses backward and reflected backward stochastic differential equations as tools for pricing. To begin with, comparison results for backward stochastic differential equations with Lipschitz driver are introduced. We price European options in a market where the randomness is modelled by the finite state Markov chain. A hedging strategy for a European option is shown to be a solution of a backward stochastic differential equation whose driver is continuous and the fair price of the option is derived as the minimal solution of such an equation. The existence of solutions and the minimal solution of the backward stochastic differential equation with continuous driver are established. We extend the backward stochastic differential approach to the so-called reflected backward stochastic differential equation, again with the Markov chain noise. This is used to find a superhedging strategy for an American option in the presence of the stochastic discount function mentioned above. Existence and uniqueness results for the solution of a reflected backward stochastic differential equation are obtained.