Perpetual cancellable American options with convertible features

Abstract

The major characteristic of the cancellable American options is the existing writer’s right to cancel the contract prematurely paying some penalty amount. The main purpose of this paper is to introduce and examine a new subclass of such options for which the penalty which the writer owes for this right consists of three parts – a fixed amount, shares of the underlying asset, and a proportion of the usual option payment. We examine the asymptotic case in which the maturity is set to be infinity. We determine the optimal exercise regions for the option’s holder and writer and derive the fair option price.

On the American style futures contracts

“…The other class of American derivatives leads to an optimal region consisting of two parts -thus a first exit from a strip arises. Such instruments are the straddle options, [1,9], their extensions named strangles, [6,12,14,15,21,22,32], cancelable American options, also known as Israeli or game options, [8,16,18,24,31,30], etc.…”

Projection and Contraction Method for Pricing American Bond Options

“…Kifer explores the scenario of a game contingent claim, drawing upon the theory of optimal stopping games [3]. Zaevski determines the optimal exercise regions for both the option's holder and writer, subsequently deriving the equitable option price [4]. Chuang develops a quasianalytical methodology to evaluate a perpetual strangle, leveraging the characteristics of the early exercise frontier in the perpetual case [5], etc.…”