Department of Quantitative Finance, Institute for Economic Research, University of Freiburg, Rempartstr. 16, 79098 Freiburg, Germany
Division of Mathematical Sciences, Nanyang Technology University, 21 Nanyang Link, 637371 Singapore, Singapore
当基本的时间离散财务模型存在歧义时，我们将调查统计套利策略。定价措施被假定为根据流动交易期权价格进行校准的mar措施，而市场数据不一定暗含该套允许的实物措施。我们的研究依赖于统计套利的数学特征，该特征最初由Bondarenko [统计套利和证券价格引入。
Financ牧师 梭哈
，2003，
16
，875-919]。与纯粹的套利策略相比，统计套利策略并非完全没有风险，但是根据特定的
σ
的结果，该概念允许人们确定平均可获利的策略。
-代数。除了表征稳健的统计套利之外，我们还提供了一个超级/子复制定理，用于构建路径依赖型期权的统计套利策略。特别是，我们表明，统计上的无套利价格的范围通常比无套利价格的范围小得多。
We investigate statistical arbitrage strategies when there is ambiguity about the underlying time-discrete financial model. Pricing measures are assumed to be martingale measures calibrated to prices of liquidly traded options, whereas the set of admissible physical measures is not necessarily implied from market data. Our investigations rely on the mathematical characterization of statistical arbitrage, which was originally introduced by Bondarenko [Statistical arbitrage and securities prices.
Rev. Financ. Stud.
, 2003,
16
, 875–919]. In contrast to pure arbitrage strategies, statistical arbitrage strategies are not entirely risk-free, but the notion allows one to identify strategies which are profitable on average, given the outcome of a specific
σ
-algebra. Besides a characterization of robust statistical arbitrage, we also provide a super-/sub-replication theorem for the construction of statistical arbitrage strategies for path-dependent options. In particular, we show that the range of statistical arbitrage-free prices is, in general, much tighter than the range of arbitrage-free prices.
