论文标题
使用选项进取的信息及其确切计算的多资产选项的无模型界限
Model-free bounds for multi-asset options using option-implied information and their exact computation
论文作者
论文摘要
我们考虑在一个周期金融市场上写下的衍生工具，并对无套利价格计算无模型上限和下限的计算感兴趣。我们在一个完全现实的环境中工作，因为我们仅假设其他单一和多资产衍生品的交易价格知识，甚至允许在这些价格中存在出现差价。我们为该市场模型提供了资产定价的基本定理，以及一个超强的二元性结果，它允许将抽象的最大化问题改于概率措施将其转变为比向量相对于向量的更可触及的最小化问题，但要受到某些约束。然后，我们将此问题重新验证为线性半侵入优化问题，并为其解决方案提供了两种算法。这些算法为$ \ varepsilon $ - 最佳的价格提供上限和下限，以及最佳定价措施的表征。这些算法是有效的，并且允许在高维情况下计算边界（例如，$ d = 60 $）。此外，这些算法可用于检测套利机会并确定相应的套利策略。使用合成和实际市场数据的数值实验展示了这些算法的效率，同时还可以通过包括已知衍生品价格的形式包括其他信息来理解模型风险的降低。
We consider derivatives written on multiple underlyings in a one-period financial market, and we are interested in the computation of model-free upper and lower bounds for their arbitrage-free prices. We work in a completely realistic setting, in that we only assume the knowledge of traded prices for other single- and multi-asset derivatives, and even allow for the presence of bid-ask spread in these prices. We provide a fundamental theorem of asset pricing for this market model, as well as a superhedging duality result, that allows to transform the abstract maximization problem over probability measures into a more tractable minimization problem over vectors, subject to certain constraints. Then, we recast this problem into a linear semi-infinite optimization problem, and provide two algorithms for its solution. These algorithms provide upper and lower bounds for the prices that are $\varepsilon$-optimal, as well as a characterization of the optimal pricing measures. These algorithms are efficient and allow the computation of bounds in high-dimensional scenarios (e.g. when $d=60$). Moreover, these algorithms can be used to detect arbitrage opportunities and identify the corresponding arbitrage strategies. Numerical experiments using both synthetic and real market data showcase the efficiency of these algorithms, while they also allow to understand the reduction of model risk by including additional information, in the form of known derivative prices.
