Optimal stopping and American options

Characterization of Optimal Stopping Regions of American Asian and Lookback Options

A general framework is developed to analyze the optimal stopping (exercise) regions of American path dependent options with either Asian feature or lookback feature. We examine the monotonicity properties of the option values and stopping regions with respect to the interest rate, dividend yield and time. From the ordering properties of the values of American lookback options and American Asian...

Optimal stopping and American options with discrete dividends and exogenous risk

In this paper we analyze some problems arising in the evaluation of American options when the underlying security pays discrete dividends. To this aim, we study the problem of maximizing the expected gain process over stopping times taking values in the union of disjoint, real compact sets. The results we obtain can be applied to evaluate options with restrictions on exercise periods, but are a...

Free boundary and optimal stopping problems for American Asian options

We give a complete and self-contained proof of the existence of a strong solution to the free boundary and optimal stopping problems for pricing American path-dependent options. The framework is sufficiently general to include geometric Asian options with nonconstant volatility and recent path-dependent volatility models.

Optimal Stopping and Applications Example 2: American options

A Comparison of Iterated Optimal Stopping and Local Policy Iteration for American Options Under Regime Switching

A theoretical analysis tool, iterated optimal stopping, has been used as the basis of a numerical algorithm for American options under regime switching [19]. Similar methods have also been proposed for American options under jump diffusion [3] and Asian options under jump diffusion [4]. We show that a re-arrangement of the numerical algorithm in the form of local policy iteration [21, 17] has p...