Free boundary and optimal stopping problems for American Asian options
نویسنده
چکیده
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.
منابع مشابه
On Asian Options of American Type
We show that the optimal stopping boundary for the early exercise Asian call option with floating strike can be characterized as the unique solution of a nonlinear integral equation arising from the early exercise premium representation (an explicit formula for the arbitrage-free price in terms of the optimal stopping boundary). The key argument in the proof relies upon a local time-space formula.
متن کاملA Note on Optimal Stopping in Models with Delay
It is known that optimal stopping problems form an important class of optimal control problems having applications in stochastic calculus (maximal inequalities), statistics (sequential analysis) and mathematical finance (American options). The results about the relationship between optimal stopping problems for Markov processes and free-boundary problems for partial differential equations often...
متن کاملOptimal 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...
متن کاملCharacterization 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...
متن کاملOn Nonlinear Integral Equations Arising in Problems of Optimal Stopping
Finite-horizon problems of optimal stopping for Markov processes have been studied by a number of authors ever since the basic principles of optimal stopping have been established in the works of Snell [16] and Dynkin [1] (for general theory see [15]). These problems are inherently two-dimensional and therefore analytically more difficult. One way to handle the problem is to formulate a free-bo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Finance and Stochastics
دوره 12 شماره
صفحات -
تاریخ انتشار 2008