使用l1-recovery的非参数和无套利的调用表面构造
Nonparametric and arbitrage-free construction of call surfaces using l1-recovery
摘要：
本文致力于应用$l_1$最小化技术来构造一个无套利看涨期权表面。我们提出了一种非参数方法来获得无模型的看涨期权表面是完全一致的市场报价和静态套利自由。该方法的灵感来自于信号处理中用于处理欠采样信号的压缩感知框架。我们解决的问题，拟合的调用选项表面稀疏的选项数据。为了说明该方法，我们继续构建整个看涨价格表面的标准普尔500期权，考虑到套利的可能性，在时间方向上。由此产生的对象是一个没有蝶式和碟式价差套利的曲面，它与原始市场点相匹配。然后，我们继续讨论外汇应用，即港元/美元看涨期权面。
英文摘要：
This paper is devoted to the application of an $l_1$ -minimisation technique to construct an arbitrage-free call-option surface. We propose a nononparametric approach to obtaining model-free call option surfaces that are perfectly consistent with market quotes and free of static arbitrage. The approach is inspired from the compressed-sensing framework that is used in signal processing to deal with under-sampled signals. We address the problem of fitting the call-option surface to sparse option data. To illustrate the methodology, we proceed to the construction of the whole call-price surface of the S\&P500 options, taking into account the arbitrage possibilities in the time direction. The resulting object is a surface free of both butterfly and calendar-spread arbitrage that matches the original market points. We then move on to an FX application, namely the HKD/USD call-option surface.
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