Making mean-variance hedging implementable in a partially observable market
Making mean-variance hedging implementable in a partially observable market
复制标题
使均值方差对冲在部分可观察的市场中可行
DOI：
10.1080/14697688.2013.867453
复制
发表时间：
2014
影响因子：
1.3
通讯作者：
Akihiko Takahashi
中科院分区：
文献类型：
--
作者：
Masaaki Fujii;Akihiko Takahashi
研究了部分可观测市场中的均值-方差套期保值问题，其中漂移过程只能通过对资产或指数过程的观测来推断。虽然大多数文献对待MVH问题的对偶方法，在这里，我们研究了一个等效的系统，由三个BSDES，并试图提供更明确的表达直接实施的从业者。在贝叶斯和Kalman-Bucy框架下，我们发现相关的贝叶斯可以通过一组简单的常微分方程产生一个半封闭的解决方案，允许快速的数值计算。这使得剩下的问题相当于解决欧洲或有债权下一个新的前瞻性措施，它是简单的，以获得前瞻性的非序贯蒙特卡罗模拟计划。我们还给出了一个特殊的例子，对冲头寸是在一个半封闭的形式。对于更一般的设置，我们提供了一个近似的对冲投资组合的渐近展开的明确表达。这些解析表达式不仅允许套期保值者在真实的时间内更新套期保值头寸，而且可以通过标准蒙特卡洛模拟直接分析套期保值组合的终端分布。
The mean-variance hedging (MVH) problem is studied in a partially observable market where the drift processes can only be inferred through the observation of asset or index processes. Although most of the literature treats the MVH problem by the duality method, here we study an equivalent system consisting of three BSDEs and try to provide more explicit expressions directly implementable by practitioners. Under the Bayesian and Kalman–Bucy frameworks, we find that a relevant BSDE can yield a semi-closed solution via a simple set of ODEs which allow quick numerical evaluation. This renders the remaining problems equivalent to solving European contingent claims under a new forward measure, and it is straightforward to obtain a forward looking non-sequential Monte Carlo simulation scheme. We also give a special example where the hedging position is available in a semi-closed form. For more generic set-ups, we provide explicit expressions of an approximate hedging portfolio by an asymptotic expansion. These analytic expressions not only allow the hedgers to update the hedging positions in real time but also make a direct analysis of the terminal distribution of the hedged portfolio feasible by standard Monte Carlo simulation.