Monte Carlo construction of hedging strategies against multi-asset European claims
Monte Carlo construction of hedging strategies against multi-asset European claims
复制标题
蒙特卡罗构建针对多资产欧洲债权的对冲策略
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
J. Schoenmakers
中科院分区：
文献类型：
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作者：
G. Milstein;J. Schoenmakers
为了评估对冲策略，我们必须随时了解相应抛物线方程（对冲投资组合的价值）及其导数（增量）的柯西问题的解。我们建议通过使用弱解方案对相应的随机微分方程组进行蒙特卡罗模拟来找到这些量。事实证明，利用同一个控制函数，可以同时实现索赔值和增量的方差减少。作为说明，我们考虑具有即时无风险储蓄债券的马尔可夫多资产模型，以及 Brace、Gatarck、Musiela 和 Jamshidian 的 LIBOR 利率模型的一些应用。
For evaluating a hedging strategy we have to know at every moment the solution of the Cauchy problem for a corresponding parabolic equation (the value of the hedging portfolio) and its derivatives (the deltas). We suggest to find these quantities by Monte Carlo simulation of the corresponding system of stochastic differential equations using weak solution schemes. It turns out that with one and the same control function a variance reduction can be achieved simultaneously for the claim value as well as for the deltas. As illustrations we consider a Markovian multi-asset model with an instantaneously riskless saving bond and also some applications to the LIBOR rate model of Brace, Gatarck, Musiela and Jamshidian.