A variational inequality arising from American installment call options pricing

Abstract

In this paper we consider a parabolic variational inequality with two free boundaries arising from American continuous-installment call options pricing. We prove the existence and uniqueness of the solution to the problem. Moreover, we obtain the monotonicity and smoothness of two free boundaries and show its numerical solution by the binomial method.

Dynkin game of convertible bonds and their optimal strategy

“…By the method in [11] or [26], we can deduce that u is the strong solution of (3.5). Moreover, (A.11) implies that ∂ x u ∈ C(Ω).…”

“…By applying the method in [11] or [26], we can prove that u n is the solution of (A.1). And (A.7)-(A.9) are the consequences of (A.4)-(A.6) as ε → 0 + .…”

Valuation of European Installment Put Option: Variational Inequality Approach

“…Moreover, we had considered the free boundary problems about American installment call option in [14] and European installment call option in [15]. Though their models are similar, their properties are different, which lead to the different methods applied to them.…”

Valuation of American strangle option: Variational inequality approach

“…Of course, Yang and Yi [13] already considered a parabolic variational inequality problem associated with the American-style continuous-installment options with two free boundaries, the lower obstacle of the variational inequality is a monotone function in spatial variables. In the present paper, variational inequality with two free boundaries does not have monotonicity condition on the lower obstacle function in (1.1).…”

“…which yields the first inequality in (2.5). For the second inequalities in (2.5), we differentiate (2.8) with respect to x, then we have 13) where…”