arXiv math/05111062005-11math.PRmath.OC

对多种资产上的某些永久美式期权和永久丹麦期权的连续性修正

Continuity corrections for certain perpetual American and Bermudan options on multiple assets

Frederik S Herzberg

备注：: 45 pages; minor improvements compared to previous version
发表信息：: Berichte aus der Mathematik, Shaker Verlag, Aachen 2006. ISBN 3-8322-5766-7

摘要：

在一个一般的Feller鞅市场中，多个资产，多维期权的最优执行区域的存在性可以通过参考Neveu的Snell包络理论来建立-而且，正如将要展示的那样，更直接地从标准鞅参数结合强马尔可夫性。在此基础上，在对数-Lévy鞅市场框架下，给出了关于永久美式期权的显式公式和渐近结果（类障碍）看跌期权价差（"连续性校正“）将被证明，在-当然，相当严格的-假设下，对数最佳锻炼区域，受到障碍，不依赖于时间网格步长，并且在平移之前是半空间。为此，Feller的Wiener-Hopf型结果将被推广到高维。它将表明，外推从确切的丹麦价格到美国的价格不能多项式的练习网格步长在许多常见的市场模型的设置，和更具体的界限上的自然标度指数的非多项式外推的一些（一维和多维）市场模型将推导。

英文摘要：

In a general Feller martingale market with several assets, the existence of optimal exercise regions for multi-dimensional Bermudan options can be established by reference to Neveu's theory of Snell envelopes -- and also, as will be shown, more directly from standard martingale arguments combined with the strong Markov property. Based on this, in the framework of a log-Lévy martingale market, explicit formulae and asymptotic results on the perpetual American-Bermudan (barrier-like) put option price difference (``continuity correction'') near the exercise boundary will be proven, under the -- of course, fairly restrictive -- assumption that the logarithmic optimal exercise region, subject to the barrier, does not depend on the time mesh size and is, up to translation, a half-space. For this sake, Wiener-Hopf type results by Feller will be generalized to higher dimensions. It will be shown that an extrapolation from the exact Bermudan prices to the American price cannot be polynomial in the exercise mesh size in the setting of many common market models, and more specific bounds on the natural scaling exponent of the non-polynomial extrapolation for a number of (both one- and multi-dimensional) market models will be deduced.

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