Multi‐asset barrier options and occupation time derivatives

A general framework is formulated to price various forms of European style multi‐asset barrier options and occupation time derivatives with one state variable having the barrier feature. Based on the lognormal assumption of asset price processes, the splitting direction technique is developed for deriving the joint density functions of multi‐variate terminal asset prices with provision for single or double barriers on one of the state variables. A systematic procedure is illustrated whereby multi‐asset option price formulas can be deduced in a systematic manner as extensions from those of their one‐asset counterparts. The formulation has been applied successfully to derive the analytic price formulas of multi‐asset options with external two‐sided barriers and sequential barriers, multi‐asset step options and delayed barrier options. The successful numerical implementation of these price formulas is demonstrated.     

Measuring the relevance of the microstructure noise in financial data

We show that the Truncated Realized Variance (TRV) of a SemiMartingale (SM) converges to zero when observations are contaminated by noise. Under the additive i.i.d. noise assumption, a central limit theorem is also proved. In consequence it is possible to construct a feasible test allowing us to measure, for a given path of a given data generating process at a given observation frequency, the relevance of the noise in the data when we want to estimate the efficient   process integrated variance IV$IV$. We thus can optimally select the observation frequency at which we can “safely” use TRV. The performance of our test is verified on simulated data. We are especially interested in the application of the test to financial data, and a comparison conducted with Bandi and Russel (2008) and Ait-Sahalia, Mykland and Zhang (2005) mean square error criteria shows that, in order to estimate IV, in many cases we can rely on TRV for lower observation frequencies than previously indicated when using Realized Variance (RV). The advantages of our method are at least two: on the one hand the underlying model for the efficient data generating process is less restrictive in that jumps are allowed (in the form of an Itô SM). On the other hand our criterion is pathwise, rather than based on an average estimation error, allowing for a more precise estimation of IV because the choice of the optimal frequency is based on the observed path. Further analysis on both simulated and empirical financial data is conducted in Lorenzini (2012) [15] and is also still in progress.     

B股相对于A股的市场投资价值研究——基于均值-方差张成与Block-Bootstrap模拟的分析

本文采用均值-方差张成的方法研究B股相对于A股的市场投资价值。首先,通过MonteCarlo模拟研究了均值-方差张成检验的小样本性质,发现模型的GMM-Wald检验存在显著的小样本偏倚,故采用基于残差再抽样的Block-Bootstrap方法模拟Wald统计量的分布以克服小样本偏倚的影响;接着分别对A、B股构造规模资产组合作为其资产的代理变量,利用模拟的Wald统计量进行实证研究,结果发现:B股未向国内居民开放前,相对于A股具有投资价值,向国内居民开放后,相对于A股不再具有投资价值。文章最后对B股投资价值的这种变化作出了经济解释,并提出相应的政策建议。     

Multivariate time changes for Lévy asset models: Characterization and calibration

We build a theoretical framework for multivariate subordination of Brownian motions, with a common and an idiosyncratic component. This follows economic intuition and introduces generalizations of some well known multivariate Lévy processes for financial applications: the compound Poisson, NIG, Variance Gamma and CGMY. In most cases we obtain the characteristic function in closed form. The extension is first kept parsimonious, by adding one parameter only. The empirical fit of (linear) dependence is then increased, by allowing for dependent Brownian motions.