Pricing the American Options from the Viewpoints of Traders - Innovative Management in Information and Production - page 296

Pricing the American Options from
the Viewpoints of Traders

Ming Long Liu and Hsuan-Ku Liu

Abstract This paper proposes an arbitrage model, which involves trading the
American option (AO) and asset in the frictionless market. The solution of this
model provides a trading strategy to maximize the expected arbitrage profit when
the market exists as an arbitrage opportunity. When there is no arbitrage opportunity
in the market, we analyze the arbitrage model by using the duality theory of
mathematical programming and show that the initial value of the AO is equal to
the expectation of all this option's future possible payoffs. Our results can be used
to construct probability recovering models from the observed market price of the
AO.

1 Introduction

An American option (AO) is a contract that can be exercised prior to the maturity.
However, an AO is always a tradable asset in the market. Instead of exercising the
AO, investors holding the ACC will trade this option in the market to maximize the
profit of the portfolio when its market price is greater than the early exercise profit.
In this paper, we will propose an arbitrage model, which involves short selling or
long buying the AO and assets, from the viewpoint of investors. Namely, the investor
in our model can reallocate the position of the AO at each state to maximize the
arbitrage profit.